Question

What is the measure of the central angle of a circle, in degrees, with radius 5 m that intercepts a 2 m arc?


a) 0.4


b) 22.9


c) 72


d) 143.2

Answer 1

Answer on Question #83355 – Math – Trigonometry

Question

What is the measure of the central angle of a circle, in degrees, with radius 5 m that intercepts a 2 m arc?

a) 0.4

b) 22.9

c) 72

d) 143.2

Solution

The radian measure $\theta$ of the central angle is the ratio of the arc length $s$ to the radius $r$.

$$\theta = \frac{s}{r}$$

Substitute

$$\theta = \frac{2}{5} \text{ rad}$$

Proportion

$180{}^{\circ}$ corresponds to $\pi$ rad

$x{}^{\circ}$ corresponds to $\frac{2}{5}$ rad

Then

$$\frac{180{}^{\circ}}{x{}^{\circ}} = \frac{\pi \text{ rad}}{\frac{2}{5} \text{ rad}} \Rightarrow x = \left(\frac{2}{5\pi}\right) 180{}^{\circ} \approx 22.9{}^{\circ}$$

Answer: b) $22.9{}^{\circ}$

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