Question 1

Solve the problem.
-Given a triangle with a = 9, b = 11,  α=31∘\alpha = 31 ^ { \circ }α=31∘  , what is (are)  the possible length(s)  of c? Round your answer to two decimal places.

Accepted Answer

A)   16.42 or 2.44
B)   16.42 or 3.41
C)   6.61
D)   14.21

Question 2

Solve the problem.
- b=4,c=6,α=80∘\mathrm { b } = 4 , \mathrm { c } = 6 , \alpha = 80 ^ { \circ }b=4,c=6,α=80∘

Accepted Answer

A)    a=7.61,β=36.6∘,γ=63.4∘\mathrm { a } = 7.61 , \beta = 36.6 ^ { \circ } , \gamma = 63.4 ^ { \circ }a=7.61,β=36.6∘,γ=63.4∘ 
B)    a=6.61,β=36.6∘,γ=63.4∘\mathrm { a } = 6.61 , \beta = 36.6 ^ { \circ } , \gamma = 63.4 ^ { \circ }a=6.61,β=36.6∘,γ=63.4∘ 
C)    a=6.61,β=63.4∘,γ=36.6∘a = 6.61 , \beta = 63.4 ^ { \circ } , \gamma = 36.6 ^ { \circ }a=6.61,β=63.4∘,γ=36.6∘ 
D)    a=5.61,β=63.4∘,γ=36.6∘a = 5.61 , \beta = 63.4 ^ { \circ } , \gamma = 36.6 ^ { \circ }a=5.61,β=63.4∘,γ=36.6∘

Question 3

Solve the problem.
-Find the area of the Bermuda Triangle if the sides of the triangle have the approximate lengths 844 miles, 921 miles, and 1,314 miles.

Accepted Answer

A)   510,414 mi
B)   386,440 mi
C)   1,545,758 mi
D)   489,843 mi

Question 4

Find the area of the triangle. If necessary, round the answer to two decimal places.
-

Accepted Answer

A)   3.52
B)   11.4
C)   235.46
D)   51.38

Question 5

Find the area of the triangle. If necessary, round the answer to two decimal places.
-A new homeowner has a triangular-shaped back yard. Two of the three sides measure 65 ft and 80 ft and form an included angle of 125°. The owner wants to approximate the area of the yard, so that he can determine the
Amount of fertilizer and grass seed to be purchased. Find the area of the yard rounded to the nearest square
Foot.

Accepted Answer

A)   5200 sq. ft
B)   2130 sq. ft
C)   4260 sq. ft
D)   2129 sq. ft

Question 6

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no
triangle at all. Solve any triangle(s)  that results.
- a=4, b=5,α=70∘\mathrm { a } = 4 , \quad \mathrm {~b} = 5 , \quad \alpha = 70 ^ { \circ }a=4, b=5,α=70∘

Accepted Answer

A)   one triangle β=34∘,γ=76∘,c=11\beta=34^{\circ}, \gamma=76^{\circ}, \mathrm{c}=11β=34∘,γ=76∘,c=11 
B)   one triangle  α=35∘,γ=75∘,c=9\alpha=35^{\circ}, \gamma=75^{\circ}, \mathrm{c}=9α=35∘,γ=75∘,c=9 
C)   one triangle β=36∘,γ=74∘,c=13\beta = 36 ^ { \circ } , \gamma = 74 ^ { \circ } , \mathrm { c } = 13β=36∘,γ=74∘,c=13 
D)   no triangle

Question 7

The displacement d (in meters)  of an object at time t (in seconds)  is given. Describe the motion of the object. What is the
maximum displacement from its resting position, the time required for one oscillation, and the frequency?
- d=−2sin⁡(5t) d = - 2 \sin ( 5 t ) d=−2sin(5t)

Accepted Answer

A)   simple harmonic;  −2 m;5πsec;5π- 2 \mathrm {~m} ; 5 \pi \mathrm { sec } ; \frac { 5 } { \pi }−2 m;5πsec;π5​  oscillations/sec
B)   simple harmonic;  2 m;25πsec;52π2 \mathrm {~m} ; \frac { 2 } { 5 } \pi \mathrm { sec } ; \frac { 5 } { 2 \pi }2 m;52​πsec;2π5​  oscillations/sec
C)   simple harmonic;  2 m;52π2 \mathrm {~m} ; \frac { 5 } { 2 \pi }2 m;2π5​  sec;  25π\frac { 2 } { 5 } \pi52​π  oscillations/sec
D)   simple harmonic;  −2 m;25πsec;52π- 2 \mathrm {~m} ; \frac { 2 } { 5 } \pi \mathrm { sec } ; \frac { 5 } { 2 \pi }−2 m;52​πsec;2π5​  oscillations/sec

Question 8

Solve the problem.
-From the edge of a 1000-foot cliff, the angles of depression to two cars in the valley below are 21° and 28°. How far apart are the cars? Round your answers to the nearest 0.1 ft.

Accepted Answer

A)   724.5 ft
B)   713.4 ft
C)   724.4 ft
D)   714.4 ft

Question 9

Find the area of the triangle. If necessary, round the answer to two decimal places.
-a = 6, b = 6, c = 7

Accepted Answer

A)   15.54
B)   17.06
C)   18.25
D)   21.14

Question 10

Solve the problem.
-A tree casts a shadow of 26 meters when the angle of elevation of the sun is 24°. Find the height of the tree to the nearest meter.

Accepted Answer

A)   10 m
B)   11 m
C)   12 m
D)   13 m

Question 11

Solve the problem.
-In flying the 81 miles from Champaign to Peoria, a student pilot sets a heading that is 9° off course and maintains an average speed of 96 miles per hour. After 15 minutes, the instructor notices the course error and
Tells the student to correct his heading. Through what angle will the plane move to correct the heading and how
Many miles away is Peoria when the plane turns?

Accepted Answer

A)   12.7°; 72.23 mi
B)   12.7°; 57.42 mi
C)   167.3°; 72.23 mi
D)   167.3°; 57.42 mi

Question 12

Solve the problem.
-Two points A and B are on opposite sides of a building. A surveyor selects a third point C to place a transit. Point C is 52 feet from point A and 68 feet from point B. The angle ACB is 53°. How far apart are points A and
B?

Accepted Answer

A)   97.2 ft
B)   107.6 ft
C)   72.1 ft
D)   55.4 ft

Question 13

Solve the problem.
-A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 90 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between
The piling and the pier is 55°. What is the distance between the piling and the pier to the nearest foot?

Accepted Answer

A)   74 ft
B)   63 ft
C)   129 ft
D)   52 ft

Question 14

Solve the problem.
-A guy wire to the top of a tower makes an angle of 64° with the level ground. At a point 26 feet farther from the base of the tower and in line with the base of the wire, the angle of elevation to the top of the tower is 27°. What
Is the length of the guy wire?

Accepted Answer

A)   38.83 ft
B)   13.13 ft
C)   51.47 ft
D)   19.61 ft

Question 15

Two sides of a right triangle ABC (C is the right angle)  are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.
-Find  tan⁡A	an \mathrm { A }tanA  when  a=2\mathrm { a } = 2a=2  and  b=9\mathrm { b } = 9b=9 .

Accepted Answer

A)    859\frac { \sqrt { 85 } } { 9 }985c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    852\frac { \sqrt { 85 } } { 2 }285c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    29\frac { 2 } { 9 }92​ 
D)    92\frac { 9 } { 2 }29​

Question 16

Find the area of the triangle. If necessary, round the answer to two decimal places.
-

Accepted Answer

A)   84.97
B)   10.55
C)   457.58
D)   40.19

Question 17

Solve the right triangle using the information given. Round answers to two decimal places, if necessary. 
- a=3,c=8;\mathrm { a } = 3 , \mathrm { c } = 8 ;a=3,c=8;  Find  b,α\mathrm { b } , \alphab,α , and  β\betaβ .

Accepted Answer

A)    b=7.42b = 7.42b=7.42  α=67.98∘\alpha = 67.98 ^ { \circ }α=67.98∘  β=22.02∘\beta = 22.02 ^ { \circ }β=22.02∘ 
B)    b=7.42b = 7.42b=7.42  α=22.02∘\alpha = 22.02 ^ { \circ }α=22.02∘  β=67.98∘\beta = 67.98 ^ { \circ }β=67.98∘ 
C)    b=8.54\mathrm { b } = 8.54b=8.54  α=23.02∘\alpha = 23.02 ^ { \circ }α=23.02∘  β=66.98∘\beta = 66.98 ^ { \circ }β=66.98∘ 
D)    b=8.54b = 8.54b=8.54  α=22.02∘\alpha = 22.02 ^ { \circ }α=22.02∘  β=67.98∘\beta = 67.98 ^ { \circ }β=67.98∘

Question 18

Find the area of the triangle. If necessary, round the answer to two decimal places.
- α=23∘,b=9,c=2\alpha = 23 ^ { \circ } , \mathrm { b } = 9 , \mathrm { c } = 2α=23∘,b=9,c=2

Accepted Answer

A)   3.52
B)   3.50
C)   3.51
D)   3.53

Question 19

Solve the problem.
-A ship sailing parallel to shore sights a lighthouse at an angle of 12° from its direction of travel. After traveling 3 miles farther, the angle is 20°. At that time, how far is the ship from the lighthouse?

Accepted Answer

A)   1.82 mi
B)   4.48 mi
C)   7.37 mi
D)   3 mi

Question 20

Accepted Answer

the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its restposition after t seconds. Also assume that the positive direction of the motion is up.An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that-a = 17; T = 5 seconds 
A)    d=−17sin⁡(25πt) d = - 17 \sin \left( \frac { 2 } { 5 } \pi t \right) d=−17sin(52​πt)  
B)    d=−17cos⁡(25πt) d = - 17 \cos \left( \frac { 2 } { 5 } \pi t \right) d=−17cos(52​πt)  
C)    d=−17cos⁡(15πt) d = - 17 \cos \left( \frac { 1 } { 5 } \pi t \right) d=−17cos(51​πt)  
D)    d=−5cos⁡(217πt) \mathrm { d } = - 5 \cos \left( \frac { 2 } { 17 } \pi \mathrm { t } \right) d=−5cos(172​πt)

Exam 7: Applications of Trigonometric Functions

Solve the problem. -A ship sailing parallel to shore sights a lighthouse at an angle of 12° from its direction of travel. After traveling 3 miles farther, the angle is 20°. At that time, how far is the ship from the lighthouse?

Correct Answer
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Find the area of the triangle. If necessary, round the answer to two decimal places. -

Correct Answer
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Solve the problem. -From the edge of a 1000-foot cliff, the angles of depression to two cars in the valley below are 21° and 28°. How far apart are the cars? Round your answers to the nearest 0.1 ft.

Correct Answer
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Solve the problem. -A guy wire to the top of a tower makes an angle of 64° with the level ground. At a point 26 feet farther from the base of the tower and in line with the base of the wire, the angle of elevation to the top of the tower is 27°. What Is the length of the guy wire?

Correct Answer
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Find the area of the triangle. If necessary, round the answer to two decimal places. - $\alpha = 23 ^ { \circ } , \mathrm { b } = 9 , \mathrm { c } = 2$

Correct Answer
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Correct Answer
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Find the area of the triangle. If necessary, round the answer to two decimal places. -

Correct Answer
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Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. -Find $\tan \mathrm { A }$ when $\mathrm { a } = 2$ and $\mathrm { b } = 9$ .

Correct Answer
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Solve the problem. - $\mathrm { b } = 4 , \mathrm { c } = 6 , \alpha = 80 ^ { \circ }$

Correct Answer
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Solve the problem. -Find the area of the Bermuda Triangle if the sides of the triangle have the approximate lengths 844 miles, 921 miles, and 1,314 miles.

Correct Answer
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Correct Answer
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Solve the problem. -Given a triangle with a = 9, b = 11, $\alpha = 31 ^ { \circ }$ , what is (are) the possible length(s) of c? Round your answer to two decimal places.

Correct Answer
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The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the maximum displacement from its resting position, the time required for one oscillation, and the frequency? - $d = - 2 \sin ( 5 t )$

Correct Answer
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Solve the problem. -Two points A and B are on opposite sides of a building. A surveyor selects a third point C to place a transit. Point C is 52 feet from point A and 68 feet from point B. The angle ACB is 53°. How far apart are points A and B?

Correct Answer
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Solve the problem. -A tree casts a shadow of 26 meters when the angle of elevation of the sun is 24°. Find the height of the tree to the nearest meter.

Correct Answer
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Find the area of the triangle. If necessary, round the answer to two decimal places. -a = 6, b = 6, c = 7

Correct Answer
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Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. - $\mathrm { a } = 4 , \quad \mathrm {~b} = 5 , \quad \alpha = 70 ^ { \circ }$

Correct Answer
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Correct Answer
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Correct Answer
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Exam 7: Applications of Trigonometric Functions

Solve the problem. -A ship sailing parallel to shore sights a lighthouse at an angle of 12° from its direction of travel. After traveling 3 miles farther, the angle is 20°. At that time, how far is the ship from the lighthouse?

Correct AnswerverifiedShow Answer

Find the area of the triangle. If necessary, round the answer to two decimal places. -

Correct AnswerverifiedShow Answer

Solve the problem. -From the edge of a 1000-foot cliff, the angles of depression to two cars in the valley below are 21° and 28°. How far apart are the cars? Round your answers to the nearest 0.1 ft.

Correct AnswerverifiedShow Answer

Solve the problem. -A guy wire to the top of a tower makes an angle of 64° with the level ground. At a point 26 feet farther from the base of the tower and in line with the base of the wire, the angle of elevation to the top of the tower is 27°. What Is the length of the guy wire?

Correct AnswerverifiedShow Answer

Find the area of the triangle. If necessary, round the answer to two decimal places. - α=23∘,b=9,c=2\alpha = 23 ^ { \circ } , \mathrm { b } = 9 , \mathrm { c } = 2α=23∘,b=9,c=2

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find the area of the triangle. If necessary, round the answer to two decimal places. -

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. -Find tan⁡A\tan \mathrm { A }tanA when a=2\mathrm { a } = 2a=2 and b=9\mathrm { b } = 9b=9 .

Correct AnswerverifiedShow Answer

Solve the problem. - b=4,c=6,α=80∘\mathrm { b } = 4 , \mathrm { c } = 6 , \alpha = 80 ^ { \circ }b=4,c=6,α=80∘

Correct AnswerverifiedShow Answer

Solve the problem. -Find the area of the Bermuda Triangle if the sides of the triangle have the approximate lengths 844 miles, 921 miles, and 1,314 miles.

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the problem. -Given a triangle with a = 9, b = 11, α=31∘\alpha = 31 ^ { \circ }α=31∘ , what is (are) the possible length(s) of c? Round your answer to two decimal places.

Correct AnswerverifiedShow Answer

The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the maximum displacement from its resting position, the time required for one oscillation, and the frequency? - d=−2sin⁡(5t) d = - 2 \sin ( 5 t ) d=−2sin(5t)

Correct AnswerverifiedShow Answer

Solve the problem. -Two points A and B are on opposite sides of a building. A surveyor selects a third point C to place a transit. Point C is 52 feet from point A and 68 feet from point B. The angle ACB is 53°. How far apart are points A and B?

Correct AnswerverifiedShow Answer

Solve the problem. -A tree casts a shadow of 26 meters when the angle of elevation of the sun is 24°. Find the height of the tree to the nearest meter.

Correct AnswerverifiedShow Answer

Find the area of the triangle. If necessary, round the answer to two decimal places. -a = 6, b = 6, c = 7

Correct AnswerverifiedShow Answer

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. - a=4, b=5,α=70∘\mathrm { a } = 4 , \quad \mathrm {~b} = 5 , \quad \alpha = 70 ^ { \circ }a=4, b=5,α=70∘

Correct AnswerverifiedShow Answer

Solve the right triangle using the information given. Round answers to two decimal places, if necessary. - a=3,c=8;\mathrm { a } = 3 , \mathrm { c } = 8 ;a=3,c=8; Find b,α\mathrm { b } , \alphab,α , and β\betaβ .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

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Find the area of the triangle. If necessary, round the answer to two decimal places. - $\alpha = 23 ^ { \circ } , \mathrm { b } = 9 , \mathrm { c } = 2$

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Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. -Find $\tan \mathrm { A }$ when $\mathrm { a } = 2$ and $\mathrm { b } = 9$ .

Correct Answer
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Solve the problem. - $\mathrm { b } = 4 , \mathrm { c } = 6 , \alpha = 80 ^ { \circ }$

Correct Answer
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Solve the problem. -Given a triangle with a = 9, b = 11, $\alpha = 31 ^ { \circ }$ , what is (are) the possible length(s) of c? Round your answer to two decimal places.

Correct Answer
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The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the maximum displacement from its resting position, the time required for one oscillation, and the frequency? - $d = - 2 \sin ( 5 t )$

Correct Answer
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Correct Answer
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Correct Answer
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Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. - $\mathrm { a } = 4 , \quad \mathrm {~b} = 5 , \quad \alpha = 70 ^ { \circ }$

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