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 - Lesson Check - Page 503: 5


In a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle, the hypotenuse is two times the shorter leg, and the longer leg is $\sqrt 3$ times the shorter leg. From the diagram, we see that the hypotenuse is not two times the shorter leg; the hypotenuse looks like it is two times the length of the longer leg instead. Additionally, the longer leg is not $\sqrt 3$ times the length of the shorter leg; instead, the shorter leg is $\sqrt 3$ times the length of the longer leg. We can see that the lengths of the longer and shorter legs have been reversed. Therefore, we must agree with Rika that the labeled lengths are not possible for this right triangle.

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