The interior angles of a triangle are 120°, 40°, and 20°. The longest side is 10 cm longer than the shorter side. Determine the perimeter of the triangle to the nearest centimetre

Answer 1

Let A = 120°, a = 10 cm; B = 40°, C = 20°,

By sine law: 10/sin120° = b/sin40°; b = 10sin40°/sin120° = 7.42227 cm

10/sin120° = c/sin20°; c = 10sin20°/sin120° = 3.94931 cm

Perimeter p = a + b + c = 10 + 7.42227 + 3.94931 = 21.37158 ≈ 21 cm

Answer 2

Draw and label a diagram

Longest (x + 10) side is opposite 120°

Shorter (x) side is opposite 40°

(x + 10) / sin 120° = x / sin 20°

Can you solve for x and answer?

Use either of those two sides and the Law of Sines to determine the length of the third side.