Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 2 - Acute Angles and Right Triangles - Section 2.1 Trigonometric Functions of Acute Angles - 2.1 Exercises - Page 53: 78a

Answer

In a $45^{\circ}$ to $45^{\circ}$ right triangle the hypotenuse has a length that is $\sqrt 2$ time as long as either leg

Work Step by Step

1. Draw a square with sides equal to k 2. Draw diagonals and label them as c. The diagonal forms two isosceles right triangles. Each angle formed by a side of the square and the diagonal measures $45^{\circ}$ 3. Using the Pythagorean theorem express c (length of the diagonal) $k^{2}+k^{2}=c^{2}$ $2k^{2} = c^{2}$ $c= \sqrt {2k^{2}}$ $c= k\sqrt {2}$ Therefore, in a $45^{\circ}$ to $45^{\circ}$ right triangle the hypotenuse has a length that is $\sqrt 2$ time as long as either leg
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