Deck 9: Applications of Trigonometry

Question 1

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Answer 1

A

Question 2

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
B, a, and c

A) Yes
B) No

Answer 2

B

Question 3

Determine the number of triangles ABC possible with the given parts.

Answer 3

D

Question 4

Determine the number of triangles ABC possible with the given parts.

Question 5

Determine the number of triangles ABC possible with the given parts.

Question 6

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
b, C, and B

A) Yes
B) No

Question 7

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
a, A, and C

A) Yes
B) No

Question 8

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
a, c, and C

A) Yes
B) No

Question 9

Determine the number of triangles ABC possible with the given parts.

Question 10

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
b, A, and B

A) Yes
B) No

Question 11

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
a, b, and C

A) Yes
B) No

Question 12

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
A, c, and a

A) Yes
B) No

Question 13

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Question 14

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
b, B, and c

A) Yes
B) No

Question 15

Determine the number of triangles ABC possible with the given parts.

Question 16

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
C, c, and A

A) Yes
B) No

Question 17

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Question 18

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Question 19

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
a, b, and c

A) Yes
B) No

Question 20

Determine the number of triangles ABC possible with the given parts.

Question 21

Find the missing parts of the triangle.

Question 22

Find the missing parts of the triangle.

Question 23

Find the missing parts of the triangle.

Question 24

Find the missing parts of the triangle.

Question 25

Solve the problem.

Question 26

Find the missing parts of the triangle.

Question 27

Find the missing parts of the triangle.

Question 28

Find the missing parts of the triangle.

Question 29

Find the missing parts of the triangle.

Question 30

Find the missing parts of the triangle.

Question 31

Find the missing parts of the triangle.

Question 32

Find the missing parts of the triangle.

Question 33

Solve the problem.

Question 34

Find the missing parts of the triangle.

Question 35

Find the missing parts of the triangle.

Question 36

Solve the problem.

Question 37

Find the missing parts of the triangle.

Question 38

Find the missing parts of the triangle.

Question 39

Find the missing parts of the triangle.

Question 40

Find the missing parts of the triangle.

Question 41

Solve the problem.

Question 42

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 43

Find the indicated angle or side. Give an exact answer.
Find the measure of angle A in degrees.

Question 44

Find the indicated angle or side. Give an exact answer.
Find the exact length of side a.

Question 45

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 46

Solve the problem.

Question 47

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 48

Assume a triangle ABC has standard labeling. Determine whether SAA, ASA, SSA, SAS, or SSS is given. Then decide
whether the law of sines or the law of cosines should be used to begin solving the triangle.
a, b, and B

A) ASA; law of cosines
B) SSA; law of sines
C) ASA; law of sines
D) SSA; law of cosines

Question 49

Find the indicated angle or side. Give an exact answer.

Question 50

Solve the problem.
A rocket tracking station has two telescopes A and B placed 2.1 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket launch. What is the
Distance to the rocket from telescope B at the moment when both tracking stations are directly east
Of the rocket telescope A reports an angle of elevation of 20° and telescope B reports an angle of
Elevation of 52°? Round to the nearest hundredth of a mile.

A) 0.91 mi
B) 1.36 mi
C) 4.84 mi
D) 3.12 mi

Question 51

Find the indicated angle or side. Give an exact answer.
Find the measure of angle A in degrees.

Question 52

Solve the problem.

Question 53

Solve the problem.

Question 54

Solve the problem.

Question 55

Solve the problem.

Question 56

Assume a triangle ABC has standard labeling. Determine whether SAA, ASA, SSA, SAS, or SSS is given. Then decide
whether the law of sines or the law of cosines should be used to begin solving the triangle.
a, c, and B

A) SAS; law of sines
B) SSA; law of sines
C) SAS; law of cosines
D) SSA; law of cosines

Question 57

Find the indicated angle or side. Give an exact answer.
Find the exact length of side a.

Question 58

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Question 59

Solve the problem.

Question 60

Find the indicated angle or side. Give an exact answer.
Find the exact length of side a.

Question 61

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 62

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Question 63

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 64

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 65

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Question 66

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 67

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Question 68

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 69

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 70

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 71

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 72

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 73

Provide an appropriate response.
Why can't the Pythagorean theorem be used to solve an oblique triangle?

Question 74

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 75

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.

Question 76

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
Two points A and B are on opposite sides of a building. A surveyor chooses a third point C 67 yd from B and 104 yd from A, with angle ACB measuring 68.3°. How far apart are A and B (to the
Nearest yard)?

A) 101 yd
B) 128 yd
C) 119 yd
D) 110 yd

Question 77

Provide an appropriate response.
State the formulas for the area of a triangle ABC that were derived using the law of sines.

Question 78

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Question 79

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Question 80

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.