In a right-angled triangle, the hypotenuse is 26 and one of the legs is 10. Find the area of the triangle.

A right-angled triangle is a triangle that has one of its angles 90 °.

To calculate the area of a triangle, we use the formula for the area behind two sides and the angle between them:

S = 1/2 a b cos α, where

a = AB = 26 cm;

b = BC = 10 cm;

cos α = cos B.

According to the cosine theorem, the cosine of an acute angle of a right-angled triangle is the ratio of the adjacent leg to the hypotenuse:

cos B = BC / AB;

cos B = 10/26 = 5/13.

S = 1/2 · 10 ∙ 26 ∙ 5/13 = 260/2 · 5/13 = 1300/26 = 50 cm2.

Answer: the area of the triangle is 50 cm2.