Question

If the hypotenuse of a 30-60-90 triangle is 20, what is the length of the longer leg? Giveanswer in exact form - NO decimal answers.

Answer 1

If the hypotenuse of this triangle 30º 60º 90º is 20, let me draw it:

The longer leg is the opposite side to the wider angle measure. So to calculate it we need this formula:

`\begin{gathered} \sin (60)=\frac{opposite\text{ side}}{\text{hypotenuse}}=(x)/(20) \\ (√(3))/(2)=(x)/(20) \\ 2x=20√(3) \\ (2x)/(2)=(20√(3))/(2) \\ x=10√(3) \end{gathered}`

Since the sine of 60º is the square root of 3/2 then we have this ratio,

therefore the answer is

x=10√3