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Chapter 1: Problem 19

Making a turn, a jetliner flies \(2.1 \mathrm{km}\) on a circular path of radius \(3.4 \mathrm{km} .\) Through what angle does it turn?

Short Answer

Expert verified
The jetliner turns through an angle of approximately 35.38 degrees.

Step by step solution

01

Recall the definition of radian measure

The radian measure of an angle in a circle is defined as the ratio of the length of the arc subtended by the angle to the radius of the circle. It could be symbolically represented as \( Angle = \frac{arc\, length}{radius} \)
02

Substitute given values into the formula

Substitute the given values into the formula: \( Angle = \frac{2.1km}{3.4km} \)
03

Calculate the angle in radians

Perform the division to find the measure of the angle in radians. This yields approximately 0.6176 radians.
04

Convert radians to degrees

Since the problem asks for the angle in degrees, convert 0.6176 radians to degrees by multiplying by \( \frac{180}{\pi} \). This yields approximately 35.38 degrees.

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