Given: ∆PQR, m∠R = 90°

Question

m∠PQR = 75°
M ∈
PR
, MP = 18
m∠MQR = 60°
Find: RQ

Answer 1

from what you know about 30-60-90 right triangles, if we let x = RQ then
MR = x√3

Now, we have

(18+x√3)/x = tan 75°

So solve for x, which is RQ.

It might help if you recall that tan75° = 2+√3