AnswersFall 24 GMS Geometry Concepts and Connections BSolving for Angle Measures of Right Triangles

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A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

Question illustration
A
16.7°
B
17.5°
C
72.5°
D
73.3°
2
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What is the approximate value of b, rounded to the nearest tenth? Use the law of sines to find the answer.

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A
1.9 units
B
4.7 units
C
5.0 units
D
5.7 units
3

The law of cosines is used to find the value of m.

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A
13
B
14
C
43
D
45
4

Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B.

Question illustration
A
183 meters
B
250 meters
C
366 meters
D
683 meters
5

A parallelogram has side lengths of 4 and 6 and an angle of measure 55°.Law of cosines: a2 = b2 + c2 – 2bccos(A)

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A
3
B
5
C
6
D
7
6

Triangle J K L is shown. Angle K L J is a right angle. The length of hypotenuse K J is 10.9 centimeters and the length of L J is 8.9 centimeters. Angle L K J is x.

Question illustration
A
cos−1 = x
Option A
B
cos−1 = x
Option B
C
sin−1 = x
Option C
D
sin−1 = x
Option D
7

The equation can be used to find the length of .

Question illustration
A
14.3 in.
B
20.5 in.
C
21.3 in.
D
22.6 in.
8

The equation can be used to find the length of .

Question illustration
A
3.0 cm.
B
9.8 cm.
C
10.5 cm.
D
12.8 cm.
9

Triangle R S T is shown. Angle T R S is a right angle. The length of R T is 5, the length of R S is 12, and the length of hypotenuse S T is 13.

Question illustration
A
Five-thirteenths
Option A
B
Five-twelfths
Option B
C
Twelve-thirteenths
Option C
D
Thirteen-twelfths
Option D
10

A beach has two floating docks. One is 650 meters east of the lifeguard stand. The other is 60° southeast and 750 meters from the lifeguard stand.Law of cosines:

Question illustration
A
589 meters
B
705 meters
C
792 meters
D
861 meters
11

Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25o angle with the ground and when the string makes a 45o angle with the ground? Round to the nearest tenth.

A
14.2 feet
B
17.1 feet
C
47.6 feet
D
55.2 feet
12

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
72 = 82 + 112 – 2(8)(11)cos(N)
B
82 = 72 + 112 – 2(7)(11)cos(M)
C
72 = 82 + 112 – 2(8)(11)cos(P)
D
82 = 72 + 112 – 2(7)(11)cos(P)
13

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 20 centimeters and the length of B C is 10.5 centimeters. Angle A B C is x.

Question illustration
A
27.7°
B
31.7°
C
58.3°
D
62.3°
14

Two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. Student A measures the angle to be 57°, and Student B measures the angle to be 46°.Law of sines:

Question illustration
A
3.0 yards
B
3.2 yards
C
3.8 yards
D
4.4 yards
15

Use the law of sines to find the value of a.Law of sines:

Question illustration
A
2.4 cm
B
2.7 cm
C
3.0 cm
D
3.3 cm

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