Solve the following problems: a Given: △PRS, RS=10 m∠P=45°, m∠S=60° Find: Perimeter of △PRS

Question

Solve the following problems:

a

Given: △PRS, RS=10

    m∠P=45°, m∠S=60°

    Find: Perimeter of △PRS

Answer 1

In ΔPRS, m∠R = 180º - 45º - 60º = 75º. Now, if you draw an altitude from ∠R to line segment PS, ∠R will split into a 45º angle and a 30º angle. I'm going to refer to the point where the altitude hits segment PS point M. Then, ΔMRS is a 30º - 60º - 90º triangle, which means that since RS = 10, MS = 5 and RM = 5√3. On the other side, we have ΔMRP, which is a 45º - 45º - 90º triangle. In which case, RM = 5√3 = MP, and therefore, PR = (5√3)(√2) = 5√6. Thus, the perimeter of ΔPRS is

P = 5√6 + 10 + 5 + 5√3

P = 15 + 5√6 + 5√3

Hope this helps

Mr. K