Trigonometry (10th Edition)

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

Chapter 2 - Acute Angles and Right Triangles - Section 2.4 Solving Right Triangles - 2.4 Exercises - Page 75: 47

Answer

$22^{\circ}$

Work Step by Step

1. We know the opposite side, and we can find the adjacent side to the angle $b = 200ft$. 2. Use the Pythagorean theorem to find the length of the diagonal of the base of the pyramid. $700^2 + 700^2 = x$ $x = 989.9 ft$ but we need only half of the length to our right triangle $a = 0.5 \times x \approx 495 ft$ 3. Use inverse of tangent to find the angle of elevation. $\tan ^{-1} \frac{200}{495}= 22^{\circ}$
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