Asked by Lily
Solve ΔPQR, given that p = 11 cm, q = 14 cm, and ∠P = 42°. If there is more than one triangle possible for the measurements provided, sketch both triangles and solve them both. Be sure to show your work.
Answers
Answered by
mathhelper
By the sine law:
sinQ/14 = sin42/11
sinQ = .85162..
∠Q = 58.39° or 121.61°
case1: ∠Q = 58.39 , the ∠R = 79.611, and
r/sin79.611 = 11/sin42
r = 11sin79.611/sin42 = 16.17
case2: ∠Q = 121.61 , the ∠R = 16.39, and
r/sin16.39 = 11/42
r = 11sin16.39/sin42 = 4.64
check my calculations
sinQ/14 = sin42/11
sinQ = .85162..
∠Q = 58.39° or 121.61°
case1: ∠Q = 58.39 , the ∠R = 79.611, and
r/sin79.611 = 11/sin42
r = 11sin79.611/sin42 = 16.17
case2: ∠Q = 121.61 , the ∠R = 16.39, and
r/sin16.39 = 11/42
r = 11sin16.39/sin42 = 4.64
check my calculations