Question

In a 30°-60°-90° right triangle, what is the length of the hypotenuse if the long leg has a length of 11√3?

Answer 1

In a 30°-60°-90° right triangle, the sides are in a specific ratio:

- The length of the short leg (opposite the 30° angle) is \( x \).
- The length of the long leg (opposite the 60° angle) is \( x\sqrt{3} \).
- The length of the hypotenuse is \( 2x \).

Given that the long leg has a length of \( 11\sqrt{3} \), we can set this equal to \( x\sqrt{3} \):

\[
x\sqrt{3} = 11\sqrt{3}
\]

To find \( x \), we divide both sides by \( \sqrt{3} \):

\[
x = 11
\]

Now we can find the hypotenuse, which is \( 2x \):

\[
\text{Hypotenuse} = 2x = 2 \cdot 11 = 22
\]

Thus, the length of the hypotenuse is

\[
\boxed{22}.
\]