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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?
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$\begingroup$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:
- $$\sin(\angle\text{A})=\frac{\text{a}}{\text{c}}\space\space\wedge\space\space\sin(\angle\text{B})=\frac{\text{b}}{\text{c}}$$
- $$\cos(\angle\text{A})=\frac{\text{b}}{\text{c}}\space\space\wedge\space\space\cos(\angle\text{B})=\frac{\text{a}}{\text{b}}$$
- $$\tan(\angle\text{A})=\frac{\text{a}}{\text{b}}\space\space\wedge\space\space\tan(\angle\text{B})=\frac{\text{b}}{\text{a}}$$
By using trigonometry or by directly using sine law i.e $sina/A=sinb/B=sinc/C$ where a,b,c are the angles and $A,B,C$ sides opposite to angles.
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