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 - Chapter Review - Page 535: 11


$x = 7$ $y = 7\sqrt 3$

Work Step by Step

The diagram is that of a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle because one angle measures $60^{\circ}$, another measures $90^{\circ}$, and the last angle must measure $30^{\circ}$. In this type of right triangle, the hypotenuse is two times the shorter leg. Let's write an equation to solve for $x$, the length of the shorter leg: $14 = 2(x)$ Divide both sides of the equation by $2$ to solve for $x$: $x = 7$ In this triangle, the longer leg is $\sqrt 3$ times the length of the shorter leg. Since we just found the length of the shorter leg, we can now set up an equation to solve for $y$, the length of the longer leg: $y = \sqrt 3(7)$ Rewrite the radical in a more standard form: $y = 7\sqrt 3$
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