Calculate side a: A= 113 degrees, Side b=25 and side c=21

Question

Using the law of sines and cosines solve the triangle.

Answer 1

Solving SAS triangle

b = 25 , c = 21 and A = 113°

Use the law of Cosines a ² = b ² + c ² -2bc Cos A

a ² = (25) ² + (21) ² - 2(25)(21)Cos(113)

a ² = 625 + 441 - 1050(-0.390)

a ² = 1066 + 409.5

a ² = 1475.5

a = 38.41

Side a = 38.41

Now to find  B , C

Use law of Sines SinB/b = SinA/a

SinB/25 = Sin(113)/38.41

SinB/25 = 0.92/38.41

SinB/25 = 0.023

SinB = 0.59

B = arc Sin (0.59)

B = 36.15°

Now we find angle C, which is easy using 'angles of a triangle add to 180°.

C = 180 -(113 + 36.15)

C = 180 -149.15

C = 30.85°

Now we have completely solved the triangle i.e. we have found all its angles and sides.

a = 38.41 , B = 36.15°, C = 30.85°.