Question

I have a diagram of a right triangle, how can I find the value os sin x and cos y?

Answer 1

Do you remember \[\sin(\theta) = \frac{ O }{ H }\]
\[\cos(\theta) = \frac{ A }{ H }\]

Answer 2

Sin(0) = Opposite/Hypotenuse and Adjacent/Hypotenuse

Answer 3

I ment cos(0) = adjacent/hypotenuse as well

Answer 4

Before we proceed, we need the Pythagorean theorem to get the length of the hypotenuse.
Can you do that?

Answer 5

Uh, a2 + b2 = c2?

Answer 6

84 If I am correct?

Answer 7

Yeah. We need c. So, \[c = \sqrt{a^{2}+b^{2}}\]
Know what a and b are?

Answer 8

The adjacent and opposite if I am correct.

Answer 9

Yes. But we need to think in terms of Pythagorean theorem now. What numbers are a and b?

Answer 10

16 and 12, we square them then add them and I believe it equals 84

Answer 11

Oh, what was I saying 84 whoops.

Answer 12

16^2 + 12^2 = 256 + 144 = 400?

Answer 13

True. Now what is the square root of 400?

Answer 14

20.

Answer 15

That means the hypotenuse is 20 units long. Now we can do sine and cosine.

Answer 16

So we will do the opposite / hypotenuse to start?

Answer 17

Opposite / hypotenuse = 0.8

Answer 18

\[\sin(y) = \frac{ 16 }{ 20 } = \frac{ 4 }{ 5 }\]

Answer 19

And I put that in decimal form am I supposed to leave it in fraction?

Answer 20

Both are fine. I just prefer fractions.

Answer 21

Cosine?

Answer 22

Square root 12 = 3.46/20 or 0.173 for cosine?

Answer 23

\[\cos(y) = \frac{ A }{ H } = \frac{ 12 }{ 20 } = \frac{ 3 }{ 5 }\]

Answer 24

Ok I understand.

Answer 25

Good!