Question

Find

(a) the value of q in radians

(b) the area of the shaded region in cm²​

Answer 1

(a) 1.18

(b) 99.71

Explanation:

to know the value of q in degrees we can use cosine of q

`\cos (q) = (OR)/(OQ)\\\\\cos (q) = (5)/(13)\\\\q = \cos^(-1)((5)/(13))\\\\q \approx 67.38`

now to radians

the formula is

`x*(2\pi)/(360)\\\\`

with x the degrees

`67.38* (2\pi)/(360)\\\\=(67.38\pi)/(180)\\\\\approx 0.374\pi\\\\\approx 1.18`

so the measure of angle q is 1.18 radians

so now for part b

`A = (r^2 \alpha )/(2)\\\\`

with
`\alpha` being the central angle in radians

for degrees is the following

`A = (\theta)/(360)* \pi r^2`

so we have

`A = (13^2 (1.18))/(2)\\\\A = 99.71`cm^2