Question

Find side AC. Round your answer to the nearest hundredth.

Answer 1

Do you know about sin, cos, and tan?

Answer 2

yes

Answer 3

Do you have an idea which one of the 3 you would need to use for this problem?

Answer 4

well i know the hypotenuse of side AC but i don't know any other side. so i guess either sin or cos?

Answer 5

Well, the question wants side AC, so you want to use the trig function that includes that hypotenuse and the missing AC side.

Answer 6

so cos?

Answer 7

Yep. So you have cos(40) = x/3 where x represents the AC side we do not know.

Answer 8

.766 = x/3 ?

Answer 9

Its usually best to get the x by itself first if possible. It makes the answer a slight bit more accurate.

Answer 10

how am i supposed to do that

Answer 11

Well, if you had x - 5 = 3, you would do the opposite and add by 5, right?

Answer 12

x = cos40/3 ?

Answer 13

You did the wrong operation. x/3 is divison by 3, so you want to do the opposite of division.

Answer 14

so x = 3/cos40

Answer 15

How did cos(40) get on bottom? :P So we have:

\[\cos(40) = \frac{ x }{ 3 } \]So when we want x by itself, we have to do opposite operations. So since we have a division of 3, we want to multiply both sides by 3
\[(3)(\cos40) = \frac{ (3)x }{ 3 }\implies 3\cos40 = x \]
Kinda make sense?

Answer 16

lol i had that when i said .766 = x/3. the next step was that.

Answer 17

the answer is 2.29

Answer 18

Right. I just meant to say that doing the multiplication of 3 first is usually more accurate. If you put 3cos(40) on your calculator, it comes out a bit more accurate then if you do cos40 = .766 then times 3. Its just a good habit I suppose xD But yeah, looks right :p So that is your side AC.

Answer 19

okay. i have a few other questions, if i post them would you be willing to help me?

Answer 20

Yeah, sure.