Question

In Triangle ABC, a = 2.4, b = 8.2, and c = 10.1. Find B to the nearest tenth.

Answer 1

What do you mean? You already have B.

Answer 2

the b they provide is just the like side i need the big B lolz

Answer 3

Does the question provide any measured angles?

Answer 4

no >.< im stuck on this one :/

Answer 5

This one's tricky. Because you know all the sides but none of the angles, you have to use the Law of Cosines (cos)
Here's the equation, just be sure you have a calculator that can solve it.
Put the angle that your finding in front of the equation to solve for it. (In the -2ac part, the variables are the angles that you are NOT solving for. So if you were solving for angle C it would be -2ab, multiply by the Cosine)
\[b ^{2}=a ^{2}+c ^{2}-2ac \cos(B)\]
So simply plug in your sides and solve all the way down, leaving the cosine for last
\[8.2^{2}=2.4^{2}+10.1^{2}-2(2.4)(10.1)\cos(B) \]
\[67.24=5.76+102.01-2(24.24)\cos(B) \]
\[67.24=107.77-48.48\cos(B) \]
-107.77 -107.77 (subtract 107.77 on both sides)
\[-40.53=-48.48\cos (B)\]
/-48.48 /-48.48 (divide by -48.48 on both sides)
\[\cos (B)=0.836014851\] (also flip the equation)
Here is where I can't help you because I don't have a calculator for it. But I think you divide by the cosine to find angle B.
Here's the link to a website that attempts to explain it.

http://www.algebra.com/algebra/homework/Triangles/Triangles.faq.question.312421.html

Good luck!