Elementary Technical Mathematics

Published by Brooks Cole
ISBN 10: 1285199197
ISBN 13: 978-1-28519-919-1

Chapter 13 - Section 13.2 - Using Trigonometric Ratios to Find Angles - Exercise - Page 546: 17


$$A=11.8°$$ $$B=78.2°$$

Work Step by Step

Find angle A. We can use the trigonometric function for sine to find angle A. $sin A=\frac{a}{c}$ $sin A=\frac{16.7m}{81.4m}$ $sin A=0.2052$ Now we solve for A by multiplying both sides of the equation by the inverse sine. So, $sin^{-1}(sin A) = sin^{-1}(0.2052)$ $A = sin^{-1}(0.2052)$ $A=11.8°$ Find angle B. We know that in right triangles the sum of the acute angles is 90°. So, $A+B=90°$ Solving for $B$, we get $B=90°-A$ $B=90°-11.8°$ $B=78.2°$
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