Find the following. (a) m∠B in degrees (b) m∠RPC in degrees (c) AC (d) CB

Question

Consider the following figure.

Given: △ABC ~ △PRC, m∠A = 62°, PC = 8, CR = 15, PR = 17, AB = 34

Find the following.

(a)

m∠B in degrees

 

(b)

m∠RPC in degrees

 

(c)

AC

(d)

CB

Answer 1

(a). m(∠B) = 90° - m(∠A) = 28°

(b). m(∠RPC) = m(∠A) = 62° by triangle similarity

(c). By similarity, AC / PC = AB / PR. So, AC / 8 = 34 / 17. AC = 16

(d). By similarity, CB / CR = AB / PR. So, CB / 15 = 34 / 17. CB = 30