Question

Find(a) the value of q in radians (b) the area of the shaded region in cm²​

Answer 1

Answer:

(a) 1.18

(b) 99.71

Step-by-step explanation:

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

$\cos (q) = \frac{OR}{OQ}\\\\\cos (q) = \frac{5}{13}\\\\q = \cos^{-1}(\frac{5}{13})\\\\q \approx 67.38$

now to radians

the formula is

$x\times\frac{2\pi}{360}$

with x the degrees

$67.38\times \frac{2\pi}{360}\\\\=\frac{67.38\pi}{180}\\\\\approx 0.374\pi\\\\\approx 1.18$

so the measure of angle q is 1.18 radians

so now for part b

$A = \frac{r^2 \alpha }{2}$

with $\alpha$ being the central angle in radians

for degrees is the following

$A = \frac{\theta}{360}\times \pi r^2$

so we have

$A = \frac{13^2 (1.18)}{2}\\\\A = 99.71$cm^2