AnswersMO-Algebra II A-CRPerforming Operations with Complex Numbers

Applying Vectors in the Plane Answers

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1
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What is the measure of angle R in shown below, given r = 10, q = 20, and Q = 100°? Round the answer to the nearest tenth. [Not drawn to scale]

Question illustration
A
0.5°
B
2.0°
C
29.5°
D
50.5°
2
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Which equation below is a true statement about ?

Question illustration
A
sine A = StartFraction h over b EndFraction
Option A
B
sine C = StartFraction a over h EndFraction
Option B
C
sine A = StartFraction h over c EndFraction
Option C
D
sine C = StartFraction h over b EndFraction
Option D
3

The diagram below shows the dimensions of a triangular park built in a new housing development. Two side lengths and one angle measure are given. [Not drawn to scale]What is the measure of angle X? Round the answer to the nearest tenth.

Question illustration
A
0.6°
B
0.8°
C
32.4°
D
50.5°
4

Which equation below is a true statement about ?

Question illustration
A
x = b minus a cosine C
Option A
B
cosine C = StartFraction h over a EndFraction
Option B
C
h = a cosine C
Option C
D
cosine C = StartFraction h over b EndFraction
Option D
5

A surveyor, Toby, measures the distance between two landmarks and the point where he stands. He also measured the angles between the landmarks in degrees. [Not drawn to scale]What is the distance, x, between the two landmarks? Round the answer to the nearest tenth.

Question illustration
A
32.5 m
B
42.1 m
C
85.1 m
D
98.5 m
6

Two construction workers, Tyrone and Diego, are standing 15 yards apart, looking up at a piano hanging between the two men from a crane. Tyrone is staring at the piano with an angle of elevation of 65°, and Diego is looking up with an angle of elevation of 77°. What is the distance between Tyrone and the piano? Round the answer to the nearest tenth. [Not drawn to scale]

Question illustration
A
9.0 yd
B
16.1 yd
C
22.1 yd
D
23.7 yd
7

Eddie solved for the length of side c in using the Law of Cosines formula, . Sophia wants to solve for the side length of b. Which equation could Sophia use to solve for the side length of b, given the other two side lengths and the measure of their included angle?

Question illustration
A
Square of b = Square of a + Square of c minus 2ac cosine C
Option A
B
Square of b = Square of a + Square of c minus 2ab cosine C
Option B
C
Square of b = Square of a + Square of c minus 2ab cosine A
Option C
D
Square of b = Square of a + Square of c minus 2ac cosine B
Option D
8

What is the length of side q, given r = 20, s = 30, and Q = 15°? Round the answer to the nearest tenth. [Not drawn to scale]

Question illustration
A
11.9
B
40.7
C
140.9
D
1659.1
9

Which equation could be used to solve for the length of side c, given a = 5, b = 12, and C = 72°? [Not drawn to scale]

Question illustration
A
square of c = square of 5 + square of 12 minus 2(5)(12) cosine 72 degree
Option A
B
square of c = square of 5 + square of 12 + 2(5)(12) cosine 72 degree
Option B
C
square of c = square of 5 minus square of 12 minus 2(5)(12) cosine 72 degree
Option C
D
square of c = square of 5 minus square of 12 + 2(5)(12) cosine 72 degree
Option D
10

Which equation represents the Law of Sines for ?

Question illustration
A
StartFraction sine A over b EndFraction = StartFraction sine B over a EndFraction
Option A
B
c Sine C = b sine B
Option B
C
StartFraction sine A over a EndFraction = StartFraction sine B over b EndFraction
Option C
D
b Sine B = a sine A
Option D
11

What is the length of side c, given a = 10, b = 8, and C = 105°? Round the answer to the nearest tenth. [Not drawn to scale]

Question illustration
A
2.3
B
8.8
C
11.1
D
14.3
12

Kyung is building a triangular pool in his backyard. He knows that side f is 12 m and that both angles G and F are 40°, which means that angle D is 100°. What is the length of side d? Round the answer to the nearest tenth. [Not drawn to scale]

Question illustration
A
7.6 m
B
7.8 m
C
18.4 m
D
19.0 m
13

In below, and . Which of the following combines the two sine ratios into one equation?

Question illustration
A
a sine C = c sine A
Option A
B
h sine C = h sine A
Option B
C
StartFraction h over sine C EndFraction = StartFraction h over sine A EndFraction
Option C
D
StartFraction sine C over a EndFraction = StartFraction sine A over c EndFraction
Option D
14

Which equation is a true statement about below?

Question illustration
A
square of h = square of a + square of b
Option A
B
square of h = square of a minus square of b
Option B
C
square of h = square of a + square of x
Option C
D
square of h = square of a minus square of x
Option D
15

To start the proof of the Law of Cosines, an altitude is constructed. Which of the following is formed due to the construction of the altitude in a non-right triangle?

A
one right triangle
B
one acute triangle
C
two right triangles
D
two acute triangles

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