# How do you find the area of triangle RST given t=15.7, s=15.7, mangleR=98?

Dec 13, 2016

$122.05$

#### Explanation:

Given that $R S = R T = 15.7 , \Delta R S T$ is isosceles.
$\implies \angle R S T = \angle R T S = \frac{180 - 98}{2} = 41$
$\implies h = 15.7 \times \sin {41}^{\circ} = 10.30$
$\implies S T = 15.7 \times \cos 41 \times 2 = 23.70$
$\implies A r e a = \frac{1}{2} \times h \times b$, where h is the height and b is the base.
$\implies A r e a = \frac{1}{2} \times 10.30 \times 23.70 = 122.05$

Alternatively, you can use the following formula to find the area :

$A r e a = \frac{1}{2} \times S {R}^{2} \times \sin \left(m \angle R\right)$
$= \frac{1}{2} \times {15.7}^{2} \times \sin {98}^{\circ} = 122.05$