Unit A: Geometry

Chapter 3: Trigonometry

Practice

Instructions: Click the Download File button to download a printable PDF of the questions. Answer each of the following practice questions on a separate piece of paper. Step by step solutions are provided under the Solutions tab. You will learn the material more thoroughly if you complete the questions before checking the answers.

Practice
Solutions

1.

Use the cosine law to find

∠ D

.

2.

Use the cosine law to find

∠ H

.

1.

Use the cosine law to find

∠ D

.

Label ΔABC.

The given information in ΔABC is

a = 70 in
b = 101 in
c = 49 in

Substitute the known sides into the cosine law to solve for

∠ C

. This version of the cosine law is used because

∠ C

must be found.

\begin{array}{rcl} \cos C & = & \frac{a^{2} + b^{2} - c^{2}}{2 a b} \\ \cos C & = & \frac{70^{2} + 101^{2} - 49^{2}}{2 (70) (101)} \\ = & \frac{4 900 + 10 201 - 2 401}{14 140} \\ = & \frac{12 700}{14 140} \\ ∠ C & = & \cos^{- 1} 0.8982 \\ = & 26 ° \end{array}

Recall: Simplify the numerator and denominator before dividing.

∠ C = ∠ D

has an angle measure of 26°.

2.

Use the cosine law to find

∠ H

.

Label ΔABC.

The given information in ΔABC is

a = 7.0 m
b = 5.7 m
c = 4.3 m

\begin{array}{rcl} \cos A & = & \frac{5 . 7^{2} + 4 . 3^{2} - 7 . 0^{2}}{2 b c} \\ \cos A & = & \frac{32.49 + 18.49 - 49}{2 (5.7) (4.3)} \\ = & \frac{1.98}{49.02} \\ = & 0.0404 \\ ∠ A & = & \cos^{- 1} 0.0404 \\ = & 88 ° \end{array}

∠ A = ∠ H

and has an angle measure of 88°.