# The law of cosines

• Jul 21st 2008, 12:10 PM
kerilynn
The law of cosines
round each angle measures to the nearest degree and side measures to the nearest tenth.

Triangle ABC, a = 15, b = 19, c = 28

i dont understand what formula to use for this geometry problem and how to set it up to work it out to get the answer
• Jul 21st 2008, 12:38 PM
Chop Suey
Take a look at the second figure here:
Image:Triangle-with-an-unknown-angle-or-side.svg - Wikipedia, the free encyclopedia

You have a, b, and c. Suppose you wanted to find the value of angle C, so you're going to have to use side c because it's opposite to angle C. Another example: if I want to find angle A, I use side a because it's the side opposite to angle a. Now, let's find angle C.

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

$\displaystyle \cos{C} = \frac{a^2 + b^2 - c^2}{2ab}$

Substitute now:
$\displaystyle \cos{C} = \frac{-198}{570}$

$\displaystyle C = \arccos{\frac{-198}{570}} = 110.326 \approx 110 \deg$

Do this again for one of the remaining angles, then find the third angle by subtracting the values of the angles you found from 180. BTW, don't use Law of Cosine, then Law of Sines. Even though it's much easier to use Law of Sines, but sometimes you might get the wrong value. It is more safer to always use Law of Cosines once you started with it.

Do you get it now?