solve the triangle C=53, a=27 and b=13.8

Question

find all missing sides and angles.

Answer 1

Given triangle sides are a = 27, b = 13.8 and angle C = 53.

Now we find angles A,B and side c.

From the law of Cosines c^2 = a^2+b^2-2abCosC

c^2 = (27)^2+(13.8)^2-2(27)(13.8)Cos(53)

c^2 = 729+190.44-745.2(0.601)

c^2 = 919.44-447.86

c^2 = 471.14

Apply squre root on each side.

Sqrt(c^2) = Sqrt(471.14)

c = 21.7

From the law of Sines a/SinA = b/SinB = c/SinC

a/SinA = c/SinC

27/SinA = 21.7/Sin(53)

27/SinA = 21.7/0.798

27/SinA = 27.2

SinA = 27/27.2

SinA = 0.99

A = Sin^-1(0.99)

A = 81.89

B = 180-(A+C)

B = 180-(82+53)

B = 45

Missing angles are B = 45, A = 82 and side c = 21.7.