The area of the right triangle is 722√3. One of the acute angles is 30 °. Find the length of the leg opposite this corner

Denote:
a – desired leg
b – second leg
c – hypotenuse
sin30 ° = 1/2 (tabular value)
sin30 ° = a / c = 1/2 (by definition of the sine)
c = 2a
By the Pythagorean theorem:
a ^ 2 + b ^ 2 = c ^ 2
a ^ 2 + b ^ 2 = (2a) ^ 2
b ^ 2 = 3a ^ 2
b = a√3
From the condition: Triangle = ab / 2 = 722√3
a * a√3 / 2 = 722√3
Reduce √3:
a ^ 2 = 722 * 2 = 1444
a = 38
Answer: a = 38