How to find the height of a right-angled triangle drawn from the vertex of a right angle if it divides

How to find the height of a right-angled triangle drawn from the vertex of a right angle if it divides the hypotenuse into segments 12 cm and 27 cm long.

1. Let’s introduce the designations of the vertices of the triangle ABC. The perpendicular to the hypotenuse will be denoted BH. The apex angle B is 90 °.

2. The length of the perpendicular drawn from the vertex of an angle equal to 90 ° to the hypotenuse is found by the formula:

BH ^ 2 = AH x CH;

BH = √AH x CH = √12 x 27 = √324 = 18 centimeters.

Answer: the length of the perpendicular BH drawn from the apex of an angle equal to 90 ° to the hypotenuse is 18 centimeters.