Question

In triangle $ghi$, we have $gh = hi = 25$ and $gi = 30$. what is $\sin\angle ghi$? (note: this is not the exact same as the previous problem!)

Answer 1

We have the following rule:
$cos (ghi)= \frac{gh^2+ih^2-gi^2}{2(gh)(ih)}\\= \frac{25^2+25^2-30^2}{2\times25\times25}=0.28$
In order to find the sine, simply do like this:
$sin(ghi)=\sqrt{1-0.28^2}=0.96$