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: 50

Answer

The distance from the top of the building to the point on the ground is 469 m

Work Step by Step

We can convert the angle to degrees: $\theta = 32^{\circ}30' = (32+\frac{30}{60})^{\circ} = 32.5^{\circ}$ Let $h$ be the height of the building. We can use $h$ and $\theta$ to find the distance $d$ from the top of the building: $\frac{h}{d} = sin(\theta)$ $d = \frac{h}{sin~\theta}$ $d = \frac{252~m}{sin~(32.5^{\circ})}$ $d = 469~m$ The distance from the top of the building to the point on the ground is 469 m
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