Solve triangle ABC given that A = 56 degrees, B = 57 degrees, and b = 9.

Question

hero · Answer

Use the fact that the interior angles of a triangle add to 180 degrees to find Angle C. 

Use law of sines to find the the lengths of sides a and c:

$$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$$

anonymous · Answer

So: sin 56/a = sin 57/9 = sin 67/c right?

hero · Answer

Yes, that appears to be correct. Now to solve for a and c, simply pair the following equations together:

$$\frac{\sin 56}{a} = \frac{\sin 57}{9}$$
$$\frac{\sin 57}{9} = \frac{\sin 67}{c}$$

hero · Answer

Make sure you are in degree mode if you use a calculator to solve.

anonymous · Answer

What do you mean degree mode?

anonymous · Answer

on your calculator there is a button that says Radians and if you click on it will say degree's where it said Radians

anonymous · Answer

I'm not finding a Radians button :/

hero · Answer

What kind of calculator do you have?

anonymous · Answer

TI 83 Plus

hero · Answer

Do you see a mode button?

anonymous · Answer

yes!

hero · Answer

Go to it and tell me what you see after clicking it.

anonymous · Answer

I see the radian / degree option and it's already on degree

anonymous · Answer

thanks so much for the help!

hero · Answer

You're welcome