# Suppose triangle ABC is isosceles, with the two equal sides being 10 cm in length and the equal angles being 40 degrees. What is the height and what is the area of the triangle?

Nov 14, 2015

$h = 10 \sin 40 , A = 50 \sin 80$

#### Explanation:

B = C = 40º

$M = \frac{B + C}{2}$

$\Delta A M C$ is a right triangle $\left(x , h , 10\right)$ = (basis, height, hypotenuse)

sin 40º = h/10

cos 40º = x/10

Area$\left(\Delta A B C\right) = \frac{1}{2} \cdot \left(2 x\right) \cdot h = 100 \sin 40 \cos 40$

We use: $\sin 2 x = 2 \sin x \cos x$