Question

If the measure of arc CB is 8/3 units, what is the measure of CAB?

Answer 1

Question:

If the measure of arc CB is $\frac{8}{3} \pi$ units, what is the measure of ∠CAB?

Answer:

120°

Step-by-step explanation:

The figure has been attached to this response.

The figure shows a circle centered at A and has a radius of 4 units.

Also, the length of the arc CB (as given in the question) is  $\frac{8}{3} \pi$ units.

The length L of an arc is given by;

L = $\frac{\beta }{360} * 2\pi * r$         -----------------(i)

Where;

β = angle subtended by the arc at the center of the circle and measured in degrees

r = radius of the circle

From the question;

β = ∠CAB

r = 4 units

L =  $\frac{8}{3} \pi$

Substitute these values into equation (i) as follows;

$\frac{8}{3} \pi$ = $\frac{\beta }{360} * 2\pi * 4$

=>  $\frac{8}{3} \pi$ = $\frac{\beta }{360} * 8\pi$

Cancel 8$\pi$ on both sides    

$\frac{1}{3}$ = $\frac{\beta }{360}$

Cross multiply

3 x β = 360 x 1

3β = 360

Divide both sides by 3

$\frac{3\beta }{3} = \frac{360}{3}$

β = 120°

Therefore, the measure of ∠CAB is 120°