Question

In `triangle TUV`, how do you express CosT in terms of t, u, v?

Answer 1

`cosT=(u^2+v^2-t^2)/(2uv)`

Explanation:

the standard cosine rule for triangle with vertices `A,B,C` is:

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

note the angle in the trig. function is the opposite angle to the side on the LHS

so if we had `CosC` to find the formula would be:

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

so if we have `DeltaTUV` and we want `cosT` we note that we start with the side `t` in the formula

`t^2=u^2+v^2-2uvcosT`

we now rearrange in terms of `cosT`

`2uvcosT=u^2+v^2-t^2`

`cosT=(u^2+v^2-t^2)/(2uv)`