how do you use the law of cosines to solve a triangle with two sides given and one angle.

Question

the triangle has side ac 25 and cb 25 and angle c being 140 degrees. Find x- side ab

Answer 1

Given sides are b = 25, a = 25 and C = 140°

In this case to solve the triangle we need to find side c and angles A,B

Use law of the cosines

c² = a²+ b²- 2ab cosC

c² = 625 + 625 - 1250 cos(140)

c² = 1250 - 1250 Cos(140)

c² = 1250 - 1250(-0.766)

c² = 1250 + 957.55

c² = 2207.55

c = Sqrt(2207.55).

c = 46.98

Now we know three sides of triangle.

From the cosine law

cosA = (b² + c²- a²)/2bc

= ( 625 + 2207.55 - 625 )/2(25)(46.98)

= 2207.55 / 2349

= 0.939

A = cos ^-1(0.939)

A = 20.11°

The sum of angles in a triangle = 180

B = 180 - (A + C)

B = 180 - (20.11 + 140)

B = 19.89°