Find the area of a right-angled triangle if the leg is 10, the hypotenuse is 20, and the acute angle is 30 degrees?

A right-angled triangle is a triangle in which one of the corners is a straight line (equal to 90º).

In order to find the area of a given triangle, we use the formula for the area behind two sides and the sine of the angle between them:

S = (a b) / 2 sin α, where:

S is the area of the triangle;

a, b – sides of the triangle;

sin α – sine of the angle between sides a and b;

sin 30º = 1/2;

S = (10 20) / 2 1/2 = 200/2 1/2 = 100/2 = 50 cm2.

Answer: the area of the triangle is 50 cm2.