Question

what is the measure of central angle aob to the nearest tenth of a degree? the measure of ∠aob is approximately ______ degrees. the solution is

Explanation:

Step1: Recall arc - length formula

The arc - length formula is $s = r\theta$, where $s$ is the arc - length, $r$ is the radius of the circle, and $\theta$ is the central angle in radians. Here, $s = 12$ inches and $r = 7$ inches.
So, $\theta=\frac{s}{r}$.

Step2: Calculate the angle in radians

Substitute $s = 12$ and $r = 7$ into the formula: $\theta=\frac{12}{7}$ radians.

Step3: Convert radians to degrees

We know that to convert radians to degrees, we use the conversion factor $\theta_{degrees}=\theta_{radians}\times\frac{180^{\circ}}{\pi}$.
So, $\theta=\frac{12}{7}\times\frac{180^{\circ}}{\pi}$.
$\theta=\frac{2160^{\circ}}{7\pi}\approx98.2^{\circ}$

Answer:

$98.2$