Answers2627 ALGEBRA II AFunction Operations

Law of Cosines Answers

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Based on the diagram below, which expression can be used to determine the distance between Seattle, WA, and San Francisco, CA? [Not drawn to scale]

Question illustration
A
StartRoot 1858 squared plus 1737 squared minus 2 (1858) (1737) cosine 21 point 4 EndRoot
Option A
B
StartRoot 1858 squared plus 1737 squared plus 2 (1858) (1737) cosine 21 point 4 EndRoot
Option B
C
1858 plus 1737 minus 2 (1858) (1737) cosine 21 point 4
Option C
D
1858 plus 1737 plus 2 (1858) (1737) cosine 21.4
Option D
2
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A ship travels 200 miles due west, then adjusts its course 30° north of west. The ship continues on this course for 30 miles. Approximately how far is the ship from where it began?

A
103.1 mi.
B
174.7 mi.
C
214.7 mi.
D
226.5 mi.
3

A 15-foot flagpole leans slightly, such that it makes an 80° angle with the ground. The shadow of the flagpole is 10 feet long when the sun has an unknown angle of elevation. How could the angle of elevation of the sun, x, be determined?

Question illustration
A
by determining the length of TV using , and then determining the value of x using
Option A
B
by determining the value of x using
Option B
C
by determining the length of TV using , and then determining the value of x using
Option C
D
by determining the value of x using
Option D
4

Four students drew four different triangles in math class. Which triangle can be solved using only the law of cosines?

Question illustration
A
Anna’s triangle
B
Yuna’s triangle
C
Carly’s triangle
D
Saki’s triangle
5

Which equation can be used to solve for x in the triangle below?

Question illustration
A
x squared equal to 4 point 7 squared plus 4 point 0 squared + 2 (4.7) (4.0) cosine 41 degree.
Option A
B
x equal to 4 point 7 plus 4 point 0 plus 2 (4.7) (4.0) cosine 41 degree.
Option B
C
x squared equal to 4 point 7 squared plus 4 point 0 squared - 2 (4.7) (4.0) cosine 41 degree.
Option C
D
x equal to 4 point 7 plus 4 point 0 minus 2 (4.7) (4.0) cosine 41 degree.
Option D
6

In triangle RST, RS = 6 cm, ST = 7 cm, and RT = 8 cm. What is the approximate measure of the largest angle in the triangle?

A
60.0°
B
63.0°
C
75.5°
D
86.6°
7

A roofer sketches a diagram of a house on which he is working. Based on the diagram, about how wide is the house?

Question illustration
A
28.5 ft.
B
37.4 ft.
C
42.9 ft.
D
56.2 ft.
8

Which equation can be used to solve for angle N in the triangle below?

Question illustration
A
6 point 2 squared equal to 3 point 6 squared plus 4 point 3 squared minus 2 (3.6) (4.3) cosine N.
Option A
B
6 point 2 squared equal to 3 point 6 squared plus 4 point 3 squared plus 2 (3.6) (4.3) cosine N.
Option B
C
6 point 2 squared equal to 3 point 6 squared plus 4 point 3 squared minus (3.6) (4.3) cosine N.
Option C
D
6 point 2 squared equal to 3 point 6 squared plus 4 point 3 squared plus (3.6) (4.3) cosine N.
Option D
9

What is the approximate measure of angle T in the triangle below?

Question illustration
A
79°
B
84°
C
96°
D
101°
10

What is the approximate length of the missing side in the triangle below?

Question illustration
A
13.9 mi.
B
19.0 mi.
C
21.3 mi.
D
25.4 mi.

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