Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 113: 63a


The radius of the curve is approximately 73.3 feet.

Work Step by Step

We can convert the angle to radians: $\theta = (42.0^{\circ})(\frac{\pi~rad}{180^{\circ}}) = 0.733~rad$ Since the chord is approximately equal to the arc length, the we can use the chord length $d$ to find the approximate value of the radius: $d \approx \theta ~r$ $r \approx \frac{d}{\theta}$ $r \approx \frac{100~ft}{0.733~rad}$ $r \approx 73.3~ft$ The radius of the curve is approximately 73.3 feet
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