[Math] calculate sides of the right triangle if I know one side and all the angles

Question

How to calculate the sides and hypotenuse length of the right triangle if I know
$ \text{bigger side} = 60$, $\text{one angle} = 60^o$ & $\text{second angle} = 30^o$ ($\text{third angle} = 90^o$)

Answer 1

You could use the identities

$$sin(\theta)=\frac{oposite-side}{hypotenuse} $$

$$cos(\theta)=\frac{adyacent-side}{hypotenuse} $$

In fact you have :

$$\sin(60)=\frac{60}{hypotenuse} \Rightarrow hypotenuse = \frac{120}{\sin(60)}=\frac{120}{\sqrt{3}}$$

and

$$\cos(60)=\frac{adyacent-side}{hypotenuse} \Rightarrow adyacent-side = \cos(60)\cdot hypotenuse =\frac{60}{\sqrt{3}} $$