# Solve the triangle?

• January 28th 2010, 07:32 AM
iluvmathbutitshard
Solve the triangle?
Use the given information to solve the triangle:
C = 85 degrees 20', a = 35. c = 50

I am confused as to how to find A, B, and b of the triangle.

Any help is appreciated.
• January 28th 2010, 08:04 AM
masters
Quote:

Originally Posted by iluvmathbutitshard
Use the given information to solve the triangle:
C = 85 degrees 20', a = 35. c = 50

I am confused as to how to find A, B, and b of the triangle.

Any help is appreciated.

Hi iluvmathbutitshard,

Try using the law of cosines.

$c^2=a^2+b^2-2ab \cos C$

$50^2=35^2+b^2-2(35)b \cos 85\frac{1}{3}$

You can solve for b here, then use that answer to solve for angle B by using the law of sines.

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

Or....

Use the law of sines to start with to find angle A.

$\frac{\sin 85\frac{1}{3}}{50}=\frac{\sin A}{35}$

Then, you'll have angle A and angle C. Easy to find angle B.

Use law of sines again to find b.

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