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 - 8-2 Special Right Triangles - Practice and Problem-Solving Exercises - Page 504: 17


$x = 5$ $y = 5 \sqrt 3$

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 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: $10 = 2x$ Divide each side by $2$ to solve for $x$: $x = 5$ 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 $y$, the length of the longer leg: $y = 5 \sqrt 3$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.