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 52: 66

Answer

$Adjacent$ = $2\sqrt2$ $Opposite$ = 2$\sqrt2$

Work Step by Step

Hypotenuse = 4 We must solve for the other sides. $\sin$ 45$^{\circ}$ = $\frac{Opposite}{Hypotenuse}$ $\sin$ 45$^{\circ}$ = $\frac{Opposite}{4}$ $\frac{\sqrt2}{2}$ = $\frac{Opposite}{4}$ 4($\frac{\sqrt2}{2}$) = $Opposite$ 2$\sqrt2$ = $Opposite$ $\tan$ 45$^{\circ}$ = $\frac{Opposite}{Adjacent}$ $\tan$ 45$^{\circ}$ = $\frac{2\sqrt2}{Adjacent}$ 1 = $\frac{2\sqrt2}{Adjacent}$ $Adjacent$ = $2\sqrt2$
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