Q:

How do I find the length of two legs in a right triangle if I know the length of the hypotenuse and the interior angles

So if I know the angles of a right triangle and I knew the hypotenuse of the triangle, how would I find the length of the other two sides?

A:

We've got this and we know $\angle\text{A}$ and $\angle\text{B}$ and $\angle\text{C}$ and $\text{c}$:

Then we get, using the Pythagorean Theorem:
$$\text{a}^2+\text{b}^2=\text{c}^2$$
And use:

$$\sin(\angle\text{A})=\frac{\text{a}}{\text{c}}\space\space\wedge\space\space\sin(\angle\text{B})=\frac{\text{b}}{\text{c}}$$
$$\cos(\angle\text{A})=\frac{\text{b}}{\text{c}}\space\space\wedge\space\space\cos(\angle\text{B})=\frac{\text{a}}{\text{b}}$$
$$\tan(\angle\text{A})=\frac{\text{a}}{\text{b}}\space\space\wedge\space\space\tan(\angle\text{B})=\frac{\text{b}}{\text{a}}$$

