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.

Find side length AB using the cosine law. Express the answer to 1 decimal place.

2.

Find side length x using the cosine law. Express the answer to the nearest tenth.

1.

Find side length AB using the cosine law. Express the answer to 1 decimal place.

Label ΔABC.

The given information in ΔABC is

\begin{array}{rcl} ∠ C & = & 49 ° \\ a & = & 672 km \\ b & = & 603 km \end{array}

Substitute these values into the cosine law to find the length of side AB, or side c.

\begin{array}{rcl} c^{2} & = & a^{2} + b^{2} - 2 a b \cos C \\ c^{2} & = & 672^{2} + 603^{2} - 2 (672) (603) \cos (49 °) \\ = & 283501.769 \\ c & = & \sqrt{283501.769} \\ = & 532.4 \end{array}

The length of side AB is 532.4 km.

Find side length x using the cosine law. Express the answer to the nearest tenth.

Label ΔABC.
Note: the triangle can be labelled differently from the diagram below as long as matching pairs are used

∠ A

is opposite side a

∠ B

is opposite side b

∠ C

is opposite side c

The given information in ΔABC is

\begin{array}{rcl} ∠ A & = & 97 ° \\ b & = & 43 in \\ c & = & 68 in \end{array}

Substitute these values into the cosine law to find the length of side BC, or side a.

\begin{array}{rcl} a^{2} & = & b^{2} + c^{2} - 2 b c \cos A \\ a^{2} & = & 43^{2} + 68^{2} - 2 (43) (68) \cos (97 °) \\ = & 7185.69192 \\ a & = & \sqrt{7185.69192} \\ = & 84.8 \end{array}

The length of side BC is 84.8 cm.