Question

How do you solve the triangle given α = 15.6 degrees, b = 10.25, and c = 5.5?

Answer 1

`a=5.17`
`B=147.7^o`
`C=16.67^o`

Explanation:

This is a side-angle-side triangle so we must use the laws of cosine.
First we'll solve for side a `a^2=b^2+c^2-2ac cosA`

`a^2=10.25^2+5.5^2-(2*10.25*5.5*cos15.6)` which gives 26.716. Take the square root of that and we have `a=5.17`

From there we can use the laws of sine `sinA/a=sinB/b=sinC/c` or we can stick with the laws of cosine `cosB=(a^2+c^2-b^2)/(2ac)`

I stuck with cosine `cosB=(5.17^2+5.5^2-10.25^2)/(2*5.17*5.5)` which gives us -0.846. Then we take `cos^-1(-0.846)=147.73^o`

We know that triangles have `180^o` so `180-15.6-147.73=12.27^o`