Question

For a circle with a diameter of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with a length of
5
2
π meters?

Answer 1

Answer:

The measurement of a central angle (in degrees) subtended by an arc is $150^{\circ \:}\:\:$.

Step-by-step explanation:

as

$d= 6$ meters

so

$r= 3$ meters

and

$Arc=\frac{5}{2}\pi$ meters

Using the formula

$\:Arc\:=r\:\theta$

$\:\frac{5}{2}\pi =3\theta$

$\mathrm{Switch\:sides}$

$3\theta =\frac{5}{2}\pi \:$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$3\theta =\frac{5\pi \:}{2}$

$\mathrm{Divide\:both\:sides\:by\:}3$

$\frac{3\theta \:}{3}=\frac{\frac{5\pi \:}{2}}{3}$

Simplify

$\theta \:=\frac{5\pi \:}{6}$

$\theta \:=\frac{5\left(180^{\circ }\right)\:}{6}$

$\theta \:=150^{\circ \:}\:\:$

Therefore, the measurement of a central angle (in degrees) subtended by an arc is $150^{\circ \:}\:\:$.