The area of a right-angled triangle is 50 √ 3 thirds. One of the acute angles is 60 °.

The area of a right-angled triangle is 50 √ 3 thirds. One of the acute angles is 60 °. Find the length of the leg opposite this corner.

The leg of a right-angled triangle located opposite an angle of 60 ° is determined by the formula:

a = (√ 3/2) * c, where “c” is the hypotenuse of the triangle.

The second leg, which is located opposite the second angle equal to 30 °, is determined through the hypotenuse “c” by the formula: в = с / 2.
Then the second leg “b” will be defined through leg “a”, as:
a / b = (√ 3/2) * c / (c / 2) = √ 3. That is, b = a / √ 3.

Determine the area of the triangle through the legs “a” and “b”.
Area = (a * b) / 2 = a * (a / √ 3) = a ^ 2/2 * √ 3 = 50 (√ 3) / 3.
Whence a ^ 2 = 100 * (√ 3) * (√ 3) / 3 = 100. Whence we find a = √ (100) = 10.