College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.3 - Geometry Essentials - R.3 Assess Your Understanding - Page 37: 45

Answer

$x=67.5 \\A=60^o \\B=95^o \\C=25^o$

Work Step by Step

RECALL: Two similar triangles have: (1) corresponding angles that are congruent; and (2) corresponding sides that are proportional Since corresponding angles are congruent, then $A=60^o \\B=95^o \\C=25^o$ Corresponding sides of similar triangles are proportional. Thus, $\dfrac{30}{20}=\dfrac{x}{45}$ Cross-multiply to obtain: $\begin{array}{ccc} &20(x) &= &30(45) \\&20x &= &1350 \\&\frac{20x}{20} &= &\frac{1350}{20} \\&x &= &67.5\end{array}$
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