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 formula for the length of an arc $s$ of a circle with radius $r$ and central - angle $\theta$ (in radians) is $s = r\theta$. Here, $s = 12$ inches and $r = 7$ inches.

Step2: Solve for $\theta$ in radians

We can rewrite the formula $s = r\theta$ as $\theta=\frac{s}{r}$. Substituting $s = 12$ and $r = 7$, we get $\theta=\frac{12}{7}$ radians.

Step3: Convert radians to degrees

To convert from radians to degrees, we use the conversion factor $\theta_{degrees}=\theta_{radians}\times\frac{180^{\circ}}{\pi}$. So, $\theta=\frac{12}{7}\times\frac{180^{\circ}}{\pi}$.
\[

$$\begin{align*} \theta&=\frac{12\times180}{7\pi}\\ &=\frac{2160}{7\pi}\\ &\approx\frac{2160}{7\times3.14159}\\ &=\frac{2160}{21.99113}\\ &\approx98.2 \end{align*}$$

\]

Answer:

$98.2$