Consider the triangle below not drawn to scale Let a 7 b 4

Consider the triangle below (not drawn to scale) Let a = 7, b = 4 and C = 120 degree. Find the length of side c and measure of the angles, A and B (in degrees). Give your answer to at least 3 decimal places.

Solution

a = 7 ; b = 4 ; Angle C = 120 deg

Use cosine rule:

c^2 = a^2 + b^2 - 2a*bcosC = 7^2 +4^2 -2*4*7cos120

c= 9.644

Use sine rule: a/sinA = c/sinC

sinA = a*sinC/c = 7*sin120/9.644 = 0.6286

Angle A = 38.947 deg

Angle B = 180 - A - C = 180 - 38.947 - 120 = 21.0534 deg