Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 11 - Section 11.3 - The Tangent Ratio and Other Ratios - Exercises - Page 512: 38


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
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.