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

Let ΔABC be a right-angled triangle, AB = 36 and BC = 39. Let us calculate the length of the leg AC using the Pythagorean formula:

BC ^ 2 = AB ^ 2 + AC ^ 2;

AC ^ 2 = BC ^ 2 – AB ^ 2;

AC = √BC ^ 2 – AB ^ 2;

AC = √39 ^ 2 – 36 ^ 2;

AC = √1521 – 1296;

AC = √225;

AC = 15.

Let’s calculate the area ΔАВС:

SΔABC = 1/2 * (AB * AC);

SΔАВС = 1/2 * (36 * 15)

SΔABC = 1/2 * 540;

SΔАВС = 270.

Answer: S∆ABC = 270.