Trigonometry (10th Edition)

Published by Pearson

Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 106: 42

Answer

The distance to the boat is approximately 845 feet.

Work Step by Step

We can express the angle in degrees: $\theta = 2^{\circ}10' = (2 + \frac{10}{60})^{\circ} = 2.17^{\circ}$ We can convert the angle to radians: $\theta = (2.17^{\circ})(\frac{\pi~rad}{180^{\circ}}) = 0.03787~rad$ Let $h$ be the height of the mast. We can approximate the distance $d$ to the boat: $h \approx \theta ~d$ $d \approx \frac{h}{\theta}$ $d \approx \frac{32~ft}{0.03787~rad}$ $d \approx 845~ft$ The distance to the boat is approximately 845 feet.

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