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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.

Sagot :

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:

[tex]\begin{gathered} \sin (60)=\frac{opposite\text{ side}}{\text{hypotenuse}}=\frac{x}{20} \\ \frac{\sqrt{3}}{2}=\frac{x}{20} \\ 2x=20\sqrt{3} \\ \frac{2x}{2}=\frac{20\sqrt{3}}{2} \\ x=10\sqrt{3} \end{gathered}[/tex]

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

therefore the answer is

x=10√3

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