# How do you solve the triangle if A= 50 degrees, B=65, a=10?

Refer to explanation

#### Explanation:

In a triangle the sum of all angles equals to 180 degrees.Hence let C be the third angle we have that

$A + B + C = 180 \implies C = 180 - A - B \implies C = 180 - 50 - 65 = {65}^{o}$

Now that we know all angles we use the law of sines which states that in a triangle we have that

$\sin \frac{A}{a} = \sin \frac{B}{b} = \sin \frac{C}{c}$

For side b we have that

$\sin \frac{A}{a} = \sin \frac{B}{b} \implies b = \sin \frac{B}{\sin} A \cdot a \implies b = \sin \frac{65}{\sin} 50 \cdot 10 = 11.83$

Because $B = C = {65}^{o}$ this makes the triangle isosceles hence
$b = c = 11.83$