Trigonometry (10th Edition)

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

Chapter 2 - Acute Angles and Right Triangles - Section 2.5 Further Applications of Right Triangles - 2.5 Exercises - Page 83: 33

Answer

The height of the pyramid is 114 feet

Work Step by Step

Let $x$ be the distance from the vertical line to the first point. We can write an expression for the height $h$: $\frac{h}{x} = tan~35.5^{\circ}$ $h = x~tan~35.5^{\circ}$ We can use the second point to write another equation for the height $h$: $\frac{h}{x+135} = tan~21.167^{\circ}$ $h = (x+135)~tan~21.167^{\circ}$ We can equate the two expressions to find $x$: $x~tan~35.5^{\circ} = (x+135)~(tan~21.167^{\circ})$ $0.713~x = 0.387~x+52.27$ $0.713~x - 0.387~x = 52.27$ $x = \frac{52.27}{0.326}$ $x = 160~ft$ We can use the first equation to find $h$: $h = x~tan~35.5^{\circ}$ $h = (160~ft)~tan~35.5^{\circ}$ $h = 114~ft$ The height of the pyramid is 114 feet
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.