Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Appendix A - Review - A.2 Geometry Essentials - A.2 Assess Your Understanding - Page A20: 42


$A=30$, $B=75$, $C=75$ and $x=8$.

Work Step by Step

Since the triangles are similar, then the angles are equal. That is $A=30$, $B=75$, $C=75$. To find $x$, we set up a ratio between corresponding sides: $$ \frac{x}{16}=\frac{6}{12}=\frac{1}{2}\Longrightarrow x=\frac{16}{2}=8 . $$
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