Question

A 30 60 90 degree triangle's hypotenuse measures 34 square root of 2. what is the measure of the longer leg

Answer 1

The figure is :

`\text{ The Hypotenuse AC= 34}\sqrt[]{2}`

Since from the property of right angle triangle, the hypotenuse is always the longest side,

So the Length of longest side is 34 square root2

For the length of BC apply the trignometric ratio of cosine

`\cos \theta=(Base)/(Hypotenuse)`

From the given data substitute the value and solve for the angle ABC

`\begin{gathered} \cos \theta=(Base)/(Hypotenuse) \\ \cos 30=\frac{BC}{34\sqrt[]{2}} \\ \frac{\sqrt[]{3}}{2}=\frac{BC}{34\sqrt[]{2}} \\ BC=\frac{34\sqrt[]{3}\sqrt[]{2}}{2} \\ BC=17\sqrt[]{6} \end{gathered}`

The length of side BC is 17 squre root 6