Question

answer please.

Answer 1

Well, do you know how to use Sine and Cosine?

Answer 2

kind of

Answer 3

Okay, let's go through it step by step. First we'll find the third side. We can use pythagorean theorem to find the last side. Do you know what that is and how to use it?

Answer 4

i know what it is but im iffy on how to use it

Answer 5

Okay, well essential our equation is this:

\[a^2+b^2=c^2\]

C will always be the hypotenuse of the triangle. Luckily, the hypotenuse is what we're trying to find. So all we have to do is substitute the other sides in for a and b. Like this:
\[35^2+12^2=C^2\]

Now just use PEMDAS, and then you'll find your C. Then square that answer to get C by itself.

Answer 6

ok i did 35squared + 12squared and got 1369

Answer 7

And now square your answer of 1369 to get your third side.

Answer 8

square it or find the square root

Answer 9

Find the square root

Answer 10

its 37

Answer 11

That's your third side, or the hypotenuse. Now we have to find the Sine and Cosine of the triangle. Do you know the equation for each of these?

Answer 12

no

Answer 13

Okay, there's a simple mnemonic we can use to remember.

SOHCAHTOA
This tells us the equation for Sine, Cosine, and Tangent

Sine:
Opposite
Hypotenuse

Cosine:
Adjacent
Hypotenuse

Tangent:
Opposite
Adjacent

Answer 14

To find sine, simply take the number OPPOSITE from the hypotenuse, and put it over the Hypotenuse

Answer 15

okay

Answer 16

?

Answer 17

And to find cosine, take the number of the side next to the hypotenuse, and put it over the hypotenuse. Whatcha get?

Answer 18

im confused put it together and ill do it

Answer 19

Okay, well let's look at the shape we have.


I put an O, A, or H depending on if it's opposite to the hypotenuse, or adjacent. Does that make it a bit simpler?

Answer 20

ok do i just press sin35 in the calculator

Answer 21

Actually scratch that, I made a tiny mistake. It depends upon the angle, so the opposite and adjacent depend upon the angle. In this case, we're trying to find the cos and sine of the angle X. Let me redraw the picture correctly.

Answer 22

ok

Answer 23

ok so i put sin12 in the calculator?

Answer 24

It really depends on your calculator, but you could probably put in sin(12/37) and get a correct answer.

Answer 25

ok

Answer 26

i think i got it wrong but i got 0.3243

Answer 27

and for cos i got 0.9459

Answer 28

Scam asked me to take over (:

But no no, that's not how we do it

Answer 29

Remember, X is the angle

When we're trying to find the opposite and adjacent sides, we always base it on the angle



So do you see that angle X, if you draw an arrow from it, that's going to be your opposite side

Answer 30

The longest side is going to be the hypotenuse! So that means that the remaining side is the ADJACENT side. Does that make sense?

Answer 31

yeah

Answer 32

So now you were supposed to find sin x and cos x

sin x = opposite / hypotenuse

cos x = adjacent / hypotenuse

and we know that the opposite side is 12
the adjacent side is 35
the hypotenuse is 37

and you have the fractions in the image

All you have to do is use a calculator and find the value of the fraction. We're not solving for x (or the angle). We're just trying to find the ratio of the sides

sin x = 12/37

so what is 12/37 = ??

Answer 33

simplify it?

Answer 34

Yeah, just use a calculator to find what 12 divided by 37 is

and we want up to 4 digits

Answer 35

i got 0.3243

Answer 36

That's correct!

Now what is

cos x = ??

remember, it's the adjacent side divided by the hypotenuse

Answer 37

0.9459

Answer 38

You got it!

Answer 39

thanks AZ

Answer 40

You're welcome!