Question

How do you solve a triangle given a=10 b=8 B=130 degrees?

Answer 1

The Law of Sines

Explanation:

The Law of Sines states

`a/(sinA)=b/(sinB)=c/(sinC)`

We are given `a` `b` and `B` so we can set them equal to each other and solve for Sin of A

`10/(sinA)` = `8/(sin130)`

manipulating that you get `(10sin130)/(8)` = `0.95755`

Taking the inverse `sin^-1(0.95755)` = `73.13`

This is the angle A. If you have 2 angles of a triangle you really have 3 angles. Just take the sum of the two known angles and subtract them from 180.

`(130+73.13)-180=23.13`

Now that you have all three angles you can use the cosine equation

`c^2=a^2+b^2-2abcosC`

`c^2=8^2+10^2- (10*8) cos23.13`

`c^2=16.86`

`sqrt(c^2)=sqrt(16.86)`

`c=4.1`

I hope that helps.