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

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

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A
18
B
22
C
29
D
41
2
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A parallelogram has side lengths of 13 and 17 and an angle that measures 64°.Law of cosines: a2 = b2 + c2 – 2bccos(A)

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A
16
B
18
C
19
D
21
3

A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point. Law of cosines:

Question illustration
A
30 degrees
B
39 degrees
C
46 degrees
D
50 degrees
4

On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder. Law of cosines:

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A
112 feet
B
125 feet
C
145 feet
D
156 feet
5

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

Question illustration
A
70°
B
77°
C
80°
D
85°
6

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

Question illustration
A
62 = p2 + 82 – 2(p)(8)cos(39°)
B
p2 = 62 + 82 – 2(6)(8)cos(39°)
C
82 = 62 + p2 – 2(6)(p)cos(39°)
D
p2 = 62 + 62 – 2(6)(6)cos(39°)
7

On which triangle can the law of cosines be applied once to find an unknown angle measure?Law of cosines: a2 = b2 + c2 – 2bccos(A)

A
Triangle X W Y is shown. Angle X Y W is a right angle. The length of hypotenuse W X is y, the length of X Y is a, and the length of W Y is 9.
Option A
B
Triangle W X Y is shown. Sides W X and X Y are congruent. The length of W Y is 7.
Option B
C
Triangle W X Y is shown. Angle X Y W is 76 degrees. The length of X Y is 5, the length of W Y is 10, and the length of W X is y.
Option C
D
Triangle W X Y is shown. The length of W X is 10, the length of X Y is 8, and the length of W Y is 16.
Option D
8

The law of cosines is used to find the measure of .

Question illustration
A
44º
B
49º
C
54º
D
59º
9

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

Question illustration
A
58°
B
64°
C
68°
D
73°
10

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

Question illustration
A
10
B
13
C
18
D
21

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