Question

Find the exact value of sinG

Answer 1

In order to do this you have to find the hypotenuse. Do you know how to do that?

Answer 2

\[A^2+B^2=C^2\]

Answer 3

Yes. So find the hypotenuse first. Let me know what you get. Ok?

Answer 4

\[4^2+12^2=X^2\]
\[16+144=X^2\]
\[160=X^2\]
\[\sqrt{160}=\sqrt{X^2}\]
\[12.64=X\]

Answer 5

Yep! Ok, now we need to find the measure of that angle. Do you know SOHCAHTOA?

Answer 6

Yes

Answer 7

Now that you know the hypotenuse, you can use either sin, cos, or tangent. I always prefer sin, but since you have the values of the sides opposite and the side adjacent, you can use tangent. That means you won't need the length of the hypotenuse that you found, but it's good to know how to do it. Use your tangent identity. Do you have a calculator?

Answer 8

i dont have a calculator

Answer 9

Ok, well I do, so you're lucky there! You tell me how to set up the identity and I will give you a value for it. What is the tangent ratio for that angle?

Answer 10

\[\tan =\frac{ Opposite }{ Adjacent}\]
\[\tan =\frac{ 4 }{ 12 }\]

Answer 11

Oh wait, back up a minute. The instructions here tell you to find the exact value of sin G. So you DO need the value of the hypotenuse. What is the sin of angle G?

Answer 12

\[\sin =\frac{ Oppoiste }{ Hypotenuse }\]
\[\sin =\frac{ 4 }{ 12.64 }\]

Answer 13

Yep. So now divide 4 by 12.65 and you will get a decimal. Do you need me to figure that out for you on my calculator or do you have a calculator on your computer that you can use?

Answer 14

i can do it in my head12.64 or 12.65

Answer 15

4/12.65 = .316455

Answer 16

Do you know how to find the sin of angle when you have this value?

Answer 17

That's supposed to be "an angle". Sorry.

Answer 18

0.00552315?

Answer 19

What is that supposed to be? The answer to 4/12.65 or the sin of the angle? Please clarify for me, ok?

Answer 20

sin of the angle

Answer 21

Ok. Actually, in order to find the sin of .316455 you need to use your calculator's inverse function in degree mode. The inverse sin of .316455 is 18.45 degrees. If you don't have a calculator, there is no way you can figure this out on your own unless you have a table or something. Either way, the answer is 18.45 degrees. If you need help understanding why this is so, I would be glad to help you.

Answer 22

i got it, so is that all i do?

Answer 23

Yep, that's it. As long as you have a calculator to help you with inverse functions, you should be good as long as you understand.

Answer 24

\[\sin \left(\tan ^{-1}\left(\frac{4}{12}\right)\right)=\frac{1}{\sqrt{10}} \]