Geometry: Common Core (15th Edition)

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

Chapter 7 - Similarity - 7-3 Providing Triangles Similar - Practice and Problem-Solving Exercises - Page 456: 15


Two angles in one triangle are congruent to two angles in the other triangle, so the triangles are similar according to the AA Similarity Postulate. $x = 180$ ft.

Work Step by Step

These two triangles are similar because two angles are congruent, so they are similar according to the AA Similarity Postulate. One angle in each triangle is a right angle, and right angles are congruent. Two angles are vertical angles; therefore, these angles are congruent because vertical angles are congruent. If two triangles are similar, then their sides are proportional. Let's find the scale factor for a pair of sides first: $\frac{90}{135}$ Divide both the numerator and denominator by their greatest common factor, $45$: $\frac{2}{3}$ This gives: $\frac{120}{x} = \frac{2}{3}$ Cross multiply to get rid of fractions: $2x = 360$ Divide each side by $2$ to solve for $x$: $x = 180$ ft.
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