Find the area of a right-angled triangle if its hypotenuse is 40 cm and the acute angle is 60 degrees.

ABC – right triangle
angle B – right angle
Angle A = 60 degrees
angle C = 30 degrees
the hypotenuse is 40 cm = AB.
Leg A B, opposite an angle of 30 degrees, is equal to half of AB – hypotenuse, that is, 40 cm / 2 = 20 cm.
using the Pythagorean theorem
leg BC squared = 40 squared – 20 squared = 1600 – 400 = 1200
leg BC = root of 1200 = 20 * root of 3
area of triangle ABC = 1/2 * leg A B * leg BC = 1/2 * 20 * 20 * root of 3 = 200 * root of 3 cm squared
S = 200 * root of 3 cm squared