Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 11 - Section 11.3 - The Tangent Ratio and Other Ratios - Exercises - Page 519: 42

Answer

The distance between the rescue and life boat is $= 2130.1$ ft.

Work Step by Step

1. Find the angle inside the small $\triangle$ $= 90 - 28$ $= 62^{\circ}$ 2.Use the tangent ratio to find the horizontal distance between the helicopter and lifeboat if they were both on the same altitude Let $x =$ distance $tan(62) = \frac{x}{1000}$ $x = 1000tan(62)$ by GDC / calculator $x = 1880.726465$ ft 3. Find the angle inside the large $\triangle$ $= 90 - 14$ $= 76^{\circ}$ 4. Use the tangent ratio to find the horizontal distance between the helicopter and the rescue boat if they were both on the same altitude Let $a = $ distance $tan(76) = \frac{a}{1000}$ by GDC / calculator $a = 4010.780934$ ft 5. Subtract the larger distance from the smaller distance to find the distance between the life boat and the rescue boat Let $d = $ distance $d = (4010.78...) - (1880.726...)$ $d = 2130.054469$ ft $d= 2130.1$ ft
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