Find the area of a right-angled triangle if its leg and hypotenuse are 36 and 39, respectively?

Given:
right-angled triangle ABC;
AB and AC – legs;
BC – hypotenuse;
AC = 36;
BC = 39.
Find the area of a right-angled triangle: S abc -?
Solution: By the Pythagorean theorem:
BC ^ 2 = AB ^ 2 + AC ^ 2;
AB ^ 2 = BC ^ 2 – AC ^ 2;
AB ^ 2 = 39 ^ 2 – 36 ^ 2;
AB ^ 2 = 1 521 – 1 296;
AB ^ 2 = 225;
AB = 15.
We know that the area of a right-angled triangle is:
S abc = 1/2 * AB * AC;
S abc = 1/2 * 15 * 36;
S abc = (1 * 15 * 36) / 2;
S abc = 15 * 18;
S abc = 270 units squared.
Answer: 270 units squared.