Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 11 - Section 11.3 - The Tangent Ratio and Other Ratios - Exercises - Page 520: 40

Answer

The tower is $\approx 203.5$ ft tall.

Work Step by Step

1. Find the angle opposite from the 270 ft length Given that this is a right angled triangle, one if the angles is $90^{\circ}$ and the other is given by the question as $37^{\circ}$ Therefore the missing angle $ = 180 - (90 + 37) = 53^{\circ}$ 2. Use the previous information in Step #1 and the sine law to solve for the height of the tower (Let $x =$ height of the tower) $\frac{270}{sin53} = \frac{x}{sin37}$ $\frac{270sin37}{sin53} = x$ $\frac{270 \times 0.6018...}{0.7986...} = x$ $\frac{162.49...}/{0.7986...} = x$ $203.459... = x$ $x \approx 203.5$ ft
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