convert angle measurement to side length when P=120 Angle A=36 B=63 and C=81

Question

Triangle side measurement where P=120 and Angles = 36, 63 & 81.

Answer 1

Given angles A = 36, B = 63, C = 81

P =120

Let the sides are a,b,c

By the law of sines the sides are in ratio Sin36, Sin63, Sin81

a = xSin(36) ---->(1)

b =  xSin(63) ----> (2)

c = xSin(81) ----> (3)

Now the perimeter P = a+b+c = 120

xSin(36)+xSin(63)+xSin(81) = 120

Take out common x from above equation.

x[Sin(36)+Sin(63)+Sin(81)] = 120

x = 120/ [Sin(36)+Sin(63)+Sin(81)]

To find length of sides substitute x in order (1),(2),(3).

a = 120/ [Sin(36)+Sin(63)+Sin(81)]*Sin(36)

a = 120Sin(36)/[Sin(36)+Sin(63)+Sin(81)]

a =120(0.5877)/[0.5877+0.8910+0.9876]

a = 70.524/2.4663

a = 28.595

b = 120/[Sin(36)+Sin(63)+Sin(81)]*Sin(63)

b = 120Sin(63)/[Sin(36)+Sin(63)+Sin(81)]

b = 120(0.8910)/[0.5877+0.8910+0.9876]

b = 106.92/2.4663

b = 43.35

c = 120/[Sin(36)+Sin(63)+Sin(81)]*Sin(81)

c = 120(Sin(81)/[Sin(36)+Sin(63)+Sin(81)]

c = 120(0.9876)/[0.5877+0.8910+0.9876]

c = 118.512/2.4663

c = 48.05

a = 28.6, b = 43.3, c = 48.1.