In a right-angled triangle ABC AC = BC Find the length of the hypotenuse if the height drawn to it is 18 cm.

AC and BC – legs, are equal by condition, so triangle ABC is isosceles, angles A and C are equal, CD is height.

The sum of the angles in the triangle is 180 °, we find the angle A:

A + B + C = 180 °.

2 × A = 180 ° – 90 °;

A = 90 °: 2 = 45 °

Let us find the length AD through tg of the angle A – the ratio of the opposite leg to the adjacent one.

In a triangle ACD CD = 18 cm (opposite leg), AD – adjacent

Tg A = CD: AD;

AD = CD × tg A ;;

AD = 18 × 1 = 18 cm.
In an isosceles triangle, the height drawn to the base divides it into two equal segments:

AB = 2 × AD = 2 × 18 = 36 cm