Question

30-60-90 , how do I get the short leg , long leg and hypotenuse

Answer 1

the given triangle is a right angle triangle.

in the right angle triangle, we know the sine rule

`\sin \theta=(perpendicular)/(hypontenuse)`
`\begin{gathered} \sin 60=(12)/(y) \\ \frac{\sqrt[]{3}}{2}=(12)/(y) \\ y=\frac{24}{\sqrt[]{3}} \end{gathered}`
`\begin{gathered} or\text{ } \\ y=\frac{24}{\sqrt[]{3}}*\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{24\sqrt[]{3}}{3} \\ y=8\sqrt[]{3} \end{gathered}`

Now cosine rule,

`\cos \theta=(base)/(hypontenuse)`
`\begin{gathered} \cos 60=\frac{x}{8\sqrt[]{3}} \\ (1)/(2)=\frac{x}{8\sqrt[]{3}} \\ x=4\sqrt[]{3} \end{gathered}`