In a right-angled triangle, one of the legs is 30, and the angle opposite to it is 45 degrees. Find the area of a right triangle

The area of a right-angled triangle is equal to half the product of its legs:

S = 1/2 * a * b.

If in a right-angled triangle one of the angles is 45 degrees, then the second angle is also 45, because the sum of the angles of the triangle is 180 degrees, the right angle is 90

180 – 90 – 45 = 45.

And if in a triangle the angles at the base are equal, then the sides lying opposite these angles are also equal.

It turns out a = b = 30, substitute these values into the area formula and calculate:

S = 1/2 * 30 * 30;

S = 1/2 * 90;

S = 45.