Question

I need help with the law of Cosine, can someone give me an example problem? It just takes a long time to do and i get lost easily.

Answer 1

Hmm,
Could you please think of two random numbers and one random angle for me?

Answer 2

11, 20, and 50 degrees

Answer 3

So Law of Cosines is:

\[c^2 = a^2+b^2 - 2abcos(C)\]

You gave:
\[a = 11\]\[b = 20\]\[C = 50\]

We're looking for little c (the side of):

Let's first plug in values that we have

Answer 4

11\[c ^{2}=11^2+20^{2}-2(11)(20)\cos(50)\]

Answer 5

ignore the 11 lol

Answer 6

That's perfect. Now all we have to do is evaluate:

\[11^2 + 20^2 = ?\]

Answer 7

521

Answer 8

\[c^2 = 521 - 2(11)(20)\cos(50)\]

I would next do 2(11)(20)

Answer 9

440

Answer 10

Now to find what cos(50) is

Answer 11

.642?

Answer 12

feels wrong

Answer 13

No, you're right .643. It's a calculus explanation but yeah lol.

\[c^2 = (521) - (441)(.643)\]

Now we just do some basic math steps

Answer 14

237.437

Answer 15

\[c^2 = 237.437\]

So last step to finding c is to root both sides, making it:

\[c = \sqrt{237.437}\]

Answer 16

15.4

Answer 17

Yep! That's the answer to that made up problem xP

Answer 18

thanks man

Answer 19

You're welcome! You can use the same steps if they ask for a or b or the angle C