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
[tex]\cos (q) = \frac{OR}{OQ}\\\\\cos (q) = \frac{5}{13}\\\\q = \cos^{-1}(\frac{5}{13})\\\\q \approx 67.38[/tex]
now to radians
the formula is
[tex]x\times\frac{2\pi}{360}\\\\[/tex]
with x the degrees
[tex]67.38\times \frac{2\pi}{360}\\\\=\frac{67.38\pi}{180}\\\\\approx 0.374\pi\\\\\approx 1.18[/tex]
so the measure of angle q is 1.18 radians
so now for part b
[tex]A = \frac{r^2 \alpha }{2}\\\\[/tex]
with [tex]\alpha[/tex] being the central angle in radians
for degrees is the following
[tex]A = \frac{\theta}{360}\times \pi r^2[/tex]
so we have
[tex]A = \frac{13^2 (1.18)}{2}\\\\A = 99.71[/tex]cm^2
