x

________________<20*
|<90*
y |
|<70*

(hypotenuse length is 12 units)

I'm learning about trig ratios, and my dad was trying to compare it to a circle or something? All I know is
sin = a/c
cos = b/c
tan = a/b

you're trying to figure out the proportions of the lengths of the triangle relative to its angles, actually the other way around in this case.

In accordance with the ratios I listed above,
side A is opposite angle A
side B is opposite angle B
side C is opposite angle C

so, in this case, the right angle is <C and the hypotenuse is side C

thus, does: ?
sin = y/12
cos = x/12
tan = y/x

Now I'm a little confused on how to bring in the angles, and how do I know whether to use sin,cos, or tan?
_______________________________________________

What happens with a problem where I know 2 of the sides, and that it's a right triangle? I then have to figure out the other two angles x and y.

I can figure out the length of the third side using the Pythagorean theorem, but how to I reverse to figure out the angular proportions from the lengths?

Thanks

your Dad is making the connection between the "unit circle" and basic trigonometry.

Do a Google search for "unit circle" or "trigonometry and the unit circle"
You will get many webpages, here is one that seems to be quite good

(Broken Link Removed)

To solve for the other two angles, x and y, in a right triangle when you know the lengths of two sides, you can use trigonometric ratios.

Let's say you know the lengths of side A and side C, and you want to find the angles.

First, you can use the Pythagorean theorem to find the length of the third side (side B) if it is unknown. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (side C) is equal to the sum of the squares of the other two sides (side A and side B). So you can use the formula:
side B = √(side C^2 - side A^2)

Once you have all three side lengths, you can use trigonometric ratios to find the angles.

For angle A:
sin(A) = opposite/hypotenuse = side A/side C
cos(A) = adjacent/hypotenuse = side B/side C
tan(A) = opposite/adjacent = side A/side B

For angle B:
sin(B) = opposite/hypotenuse = side B/side C
cos(B) = adjacent/hypotenuse = side A/side C
tan(B) = opposite/adjacent = side B/side A

For the given triangle:
sin(A) = y/12
cos(A) = x/12
tan(A) = y/x

Now, to determine which trigonometric ratio to use, think about what you are trying to solve. If you know the length of the opposite side and the hypotenuse, use sine (sin) ratio. If you know the length of the adjacent side and the hypotenuse, use cosine (cos) ratio. If you know the length of the opposite side and the adjacent side, use tangent (tan) ratio.

In this case, since you know the lengths of side A and side C, and you want to find angle A and angle B, you can use sin and cos ratios as follows:
sin(A) = y/12
cos(A) = x/12

By applying trigonometric functions, you can solve for the angles A and B.

I hope this helps you understand how to use trigonometric ratios to find angles in a right triangle!