how to solve triangle of a=17, b=22, c=25 this is for college trigonometry

Question

I understand everything up until how to get the approximate value.

Answer 1

Given three sides of triangle a = 17, b = 22, c= 25

Use the law of cosines

First to find the one of the angle of given triangle.

Let's find the angle CosA = (b^2+c^2-a^2)/2bc

CosA = (484+625-289)/1100

CosA = 820/1100

CosA = 0.7454

A = Cos^-1(0.7454)

A = 41.8065

Next we will find another angle CosB = (c^2+a^2-b^2)/2ca

CosB = (625+289-484)/850

CosB = 430/850

CosB = 0.5058

B = Cos^-1(0.5058)

B = 59.61

Finally we find angle C =180-(59.61+41.80)

C = 78.59

Now we have completly solved the triangle A =41.8, B = 59.61, C = 78.59.