Question

an arc of length 40 ft subtends a central angle θ in a circle of radius 48 ft. find the measure of θ in radians.
θ = 0.833 ×! rad
find the measure of θ in degrees. (round your answer to one decimal place.)
θ = 47.7 √ °
resources
read it watch it
submit answer

1. - / 1 points 0/12 submissions used

this exercise involves the formula for the area of a circular sector.
find the area a of the sector shown in each figure.
(a)

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 $s = r\theta$.
We know that $s = 40$ ft and $r = 48$ ft. So, $\theta=\frac{s}{r}$.

Step2: Calculate $\theta$ in radians

Substitute $s = 40$ and $r = 48$ into the formula: $\theta=\frac{40}{48}=\frac{5}{6}\approx0.8333\cdots\approx0.8$ rad.

Step3: Convert radians to degrees

The conversion formula from radians to degrees is $\theta_{degrees}=\theta_{radians}\times\frac{180^{\circ}}{\pi}$.
Since $\theta=\frac{5}{6}$ radians, then $\theta_{degrees}=\frac{5}{6}\times\frac{180^{\circ}}{\pi}=\frac{150^{\circ}}{\pi}\approx47.7^{\circ}$.

Answer:

The measure of $\theta$ in radians is $\frac{5}{6}\approx0.8$ rad.
The measure of $\theta$ in degrees is approximately $47.7^{\circ}$.