# How do you solve the triangle when a=7, b=9, A=34?

Jan 31, 2016

B = 45.96 , C = 100.03 , c = 12.326

#### Explanation:

Use sin rule of triangles

If a, b, c are sides of a triangle and angles opposite to them are A, B, C respectively then

$\frac{\sin \left(A\right)}{a} = \frac{\sin \left(B\right)}{b} = \frac{\sin \left(C\right)}{c} = k$ (any constant)

Using this we get

$\frac{\sin \left(34\right)}{7} = \frac{\sin \left(B\right)}{9}$

B = 45.96

Now $C = 180 - \left(A + B\right)$

C = 100.03

Now using

$\frac{\sin \left(B\right)}{b} = \frac{\sin \left(C\right)}{c}$

c = 12.326