Trigonometry Problem about the Area of a triangle (given one side and two angles)

Question

Find the area of (triangle) TRI if TR=10cm, m∠T=105°and m∠R=30°

Answer 1

Opposite angle to given side is θ = 180° - ( 105° + 30°) = 45°.

By sine law 10/sin45° = x/sin30°; x = 10si30°/sin45° = 5√2 cm.

Now area A of triangle: A = 1/2·10·5√2·sin105° = 34.15 cm².