Question

All I really need help with on this is what steps would I take to find the length of the hypotenuse? I know how to do the rest of it, it's pretty easy past that point.

Use the image below to answer the following question. Find the value of sin x° and cos y°. What relationship do the ratios of sin x° and cos y° share?
http://prntscr.com/9wizsl

Answer 1

hint:
we can write this:
\[\large \begin{gathered}
hypotenuse = \sqrt {{4^2} + {3^2}} = ...?\quad \left( {theorem\;of\;Pitagora} \right) \hfill \\
\hfill \\
3 = hypotenuse \cdot \sin x \hfill \\
\hfill \\
\cos y = \cos \left( {90 - x} \right) = \cos 90\cos x + \sin 90\sin x = ...? \hfill \\
\end{gathered} \]

Answer 2

I get the first part (I was already trying that but wasn't sure if it was correct), but the rest of it doesn't make sense to me? That's not how I just learned all of this and it confuses me.

Answer 3

I figured that, after finding the hypotenuse, you'd simply use that to complete sin x and cos y and their relationship was that they'd come out to be the same?

Answer 4

yes!
if we complete my last formula, we get:
\[\large \begin{gathered}
\cos y = \cos \left( {90 - x} \right) = \cos 90\cos x + \sin 90\sin x = \hfill \\
\hfill \\
= 0 \cdot \cos x + 1 \cdot \sin x = \sin x \hfill \\
\end{gathered} \]

Answer 5

so doing the √4^2 + 3^2 would give me the hypotenuse, correct?

Answer 6

yes!

Answer 7

Okay, so the hypotenuse is 5

Answer 8

that's right!

Answer 9

Thank you!

Answer 10

:)