Help with a sin degree problem please.

[4boysmeme]

Use the figure to find sin x degree.

I don't even know how where to start on this problem. Please solve this for me. We will have a test on this next week and I need step by step instructions. I am totally lost. Thank you.

 

[tkhunny]

You already started! Excellent drawing.

Ponder the three equal half-diagonals. Think about the upper-right quadrant. It's a right triangle with equal legs and an hypotenuse of 8.

That's enough to be almost done. Shout out the length of the two legs!! Come on, just let it out.

 

[4boysmeme]

That is where I get lost. I know that the two sides are the same length and that a squared + b squared = 8 squared, but I can't come up with the length of each of the other two sides. I think my brain is just dead from working on this for so long...........

 

[4boysmeme]

Ok after much deliberation I have come up with x to be approximately 34.44990199. Can you tell me if this is correct, please.

 

[wjm11]

I have come up with x to be approximately 34.44990199.

That is correct; however, keep in mind that in your problem statement,

Use the figure to find sin x degree.

you were to find sin x, not x itself.

 

[4boysmeme]

Now I am confused. Isn't that what I found?

 

[Mrspi]

Now I am confused. Isn't that what I found?

I don't think so.

You have a right triangle.

The hypotenuse of that right triangle has length 10. One acute angle has degree measure x. The leg OPPOSITE that angle has length 4 sqrt(2).

The right triangle definition of sin x where x is an acute angle in a right triangle is:

sin x = (opposite leg) / (hypotenuse)


Substitute 4 sqrt(2) for the opposite leg, and 10 for the hypotenuse. Simplify that ratio if possible.

That will be "sin x"