In a right-angled triangle, the area is 72√3, one of the acute angles is 30 degrees. Find the leg.

Let’s write down the value of the sine of an angle of 30 degrees:

sin 30о = 1/2.

Since the sine is the ratio of the opposite leg to the hypotenuse, this leg is equal to half of the hypotenuse. Based on this, according to the Pythagorean theorem, you can find the value of the second leg:

a2 = b2 + c2 →

b = √ (a2 – c2) = √ (22 – 12) = √ (4 – 1) = √ (3).

Let’s write the formula for the area of a right-angled triangle:

S = (ab) / 2 →

a = (2S) / b = (2 * 72√ (3)) / (√ (3)).

Reduce the resulting fraction:

a = 2 * 72 = 144 – leg length.

Answer: 144.