Algebra 2 (1st Edition)

Published by McDougal Littell

Chapter 13, Trigonometric Ratios and Functions - 13.1 Use Trigonometry with Right Triangles - 13.1 Exercises - Skill Practice - Page 857: 22

Answer

$c \approx 19.94$ $b \approx 15.92$ $\angle A=37^{\circ}$

Work Step by Step

$\sin 37^{\circ}=\dfrac{Opposite}{Hypotenuse}=\dfrac{12}{c}$ This gives: $c \approx 19.94$ and $\tan 37^{\circ}=\dfrac{Opposite}{Adjacent}=\dfrac{12}{b}$ This gives: $b \approx 15.92$ Since the triangle is $180^{\circ}$ and the right angle is $90^{\circ}$: $\angle A=\angle C-\angle B$ This gives: $\angle A=90^{\circ}-53^{\circ}=37^{\circ}$

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