# How do you find the area of triangle PQR given p=212, q=287, mangleR=124^@?

Apr 19, 2018

We can choose either side to compute the height of the triangle; I shall choose $p$:

$\text{Height} = p \sin \left(R\right)$

Substitute $p = 212$ and $R = {124}^{\circ}$:

$\text{Height} = 212 \sin \left({124}^{\circ}\right)$

$\text{Height} \approx 175.8$

The area of the triangle is:

$\text{Area" = 1/2"Base" xx "Height}$

By choosing $p$ for the computation of the height, we have forced the choice of the base to be $q$. Substitute $\text{Base = 287}$ and $\text{Height} \approx 175.8$:

$\text{Area} = \frac{1}{2} 287 \times 175.8$

$\text{Area} = 25227.3$

I will leave it to you to show that you obtain the same area if you choose $q$ to compute the height and $p$ to the base.