Find the missing parts of the triangle A 961 degree b 152

Find the missing parts of the triangle. A = 96.1 degree b = 15.2 ft a = 30.4 ft

Solution

Using the cosine law,

c² = a² + b² 2ab cosA

c² = 30.4^2 + 15.2^2 - 2*30.4*15.2cos96.1

c = 35.4 ft

Now, sine law,

sin B / b = sin A / a = sin 96.1/30.4

=> sin B = 0.497

B = arcsin (0.497) = 29.8 deg

Therefore angle C = 180 - (96.1 + 29.8) = 54.1 deg