Find the area of a right-angled triangle if the hypotenuse is 29 cm and one of the boats is 21 cm.

Given:
ABC – right triangle,
AB – hypotenuse,
AB = 29 centimeters,

AC = 21 centimeters.

Find the area S abc -?
Solution:
1) Consider a right-angled triangle ABC. Then, by the Pythagoras theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):
AC ^ 2 + BC ^ 2 = AB ^ 2;

BC ^ 2 = AB ^ 2 – AC ^ 2;

BC ^ 2 = 841 – 441;

BC ^ 2 = 400;

BC = 20 centimeters.

2) S abc = 1/2 * AC * BC;
S abc = 1/2 * 21 * 20;
S abc = 21 * 10;
Savs = 210 square centimeters – the area of the triangle ABC.
Answer: 210 square centimeters.