Question

Use the Law of Sines to find the missing angle of the triangle. Find measure of angle b given that c=83 , a=44 and that measure of angle a =31 . A=76.3 degrees B= 15.8 degrees C= 72.7 degrees,

Answer 1

- Use the Law of SInes to find the measure of angle C:
(sinC)/c = (sinA)/a
sincC = c(sinA)/a
C = sin⁻¹(c·sinA / a)

Plugging in numbers:
C = sin⁻¹(83·sin(31) / 44)
   = sin⁻¹(0.97155) 
   = 76.3°
- We know that the sum of the internal angles of a triangle is 180°, therefore:
B = 180 - (A + C) 
   = 180 - (31 + 76.3)
   = 180 - 107.3
   = 72.7°

- Therefore the corret answer is C: angle B is 72.7°