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: 16

Answer

The hypotenuse is $112$ cm.

Work Step by Step

The diagram is that of a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle because one angle measures $30^{\circ}$, another measures $90^{\circ}$, and the last angle measures $60^{\circ}$. In this triangle, the longer leg is $\sqrt 3$ times the length of the shorter leg. Let's set up that equation to solve for $x$, the length of the shorter leg: $56\sqrt 3 = \sqrt 3 • x$ Divide both sides by $\sqrt 3$: $x = 56$ In this type of right triangle, the hypotenuse is two times the shorter leg. Let's write an equation to solve for $y$, the length of the hypotenuse: $y = 2(56)$ Multiply to solve for $y$: $y = 112$ The hypotenuse is $112$ cm.
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