Question

select the correct answer.
the longer leg of a right triangle has a length of 15. one angle in the triangle is 60 degrees. what is the length of the shortest leg?
$5\sqrt{3}$
$15\sqrt{3}$
$10\sqrt{3}$
5

Explanation:

Step1: Define triangle sides/angles

In a right triangle with a 60° angle, the angles are 90°, 60°, 30°. The longer leg (opposite 60°) is 15, shortest leg (opposite 30°) = $x$.

Step2: Use tangent ratio

$\tan(60^\circ) = \frac{\text{longer leg}}{\text{shortest leg}}$
$\tan(60^\circ) = \sqrt{3}$, so:
$\sqrt{3} = \frac{15}{x}$

Step3: Solve for $x$

Rearrange to isolate $x$:
$x = \frac{15}{\sqrt{3}}$
Rationalize the denominator:
$x = \frac{15\sqrt{3}}{3} = 5\sqrt{3}$

Answer:

$5\sqrt{3}$