15 remember these two formulas: tan (a+b) = (tana+tanb)/(1-tana * tanb).

tan(A-B)=(tanA-tanB)/( 1+tanA * tanB)

∠BPC=∠ACP+∠CAP (the outer angle of a triangle is equal to the sum of two non-adjacent inner angles)

tan∠CAP=BC/AC= 1/3

TanACP= 1 (because it is 45).

The results came out.

Question 16:

The length of AE is fixed and can be calculated by Pythagorean theorem.

PQ is fixed and equal to 3.

BP=5-CQ, the key is to calculate when the value of AP+QE is the minimum. Both AP and QE calculate an algebraic expression expressed by the length of CQ through Pythagorean theorem, and what the value of CQ should be when finding the minimum.