Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 8 - Right Triangles and Trigonometry - Common Core Cumulative Standards Review - Selected Response - Page 540: 13


$x = 28$

Work Step by Step

The two triangles are similar because of the AA Similarity Postulate, which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In similar triangles, corresponding angles are congruent and corresponding sides are proportional. The corresponding angles are already congruent; therefore, we need to make corresponding sides proportional. Let us set up the proportion for the corresponding sides: $\frac{3}{21} = \frac{4}{x}$ Use the cross products property to eliminate the fractions: $3x = 84$ Divide both sides by $3$ to solve for $x$: $x = 28$
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