In a right-angled triangle, the legs are 8√2 cm. Find the height dropped from the top of the right angle.

1. Let us introduce the designations for the vertices of the triangle ABC. BH is the height drawn to the AC hypotenuse.

The apex angle B is 90 °.

2. Since, according to the condition of the problem, the legs AB and BC are equal, the triangle ABC is isosceles. Corners

BAC and ACB are equal.

3. We calculate the value of each of these angles:

(180 ° – 90 °) / 2 = 45 °.

4. Calculate the length BH:

BH / AB = sine of the angle BAC. Sine of an angle 45 ° = √2 / 2. AB = 8√2 according to the problem statement.

BH / AB = √2 / 2.

BH = 8√2 x √2 / 2 = 8 x 2/2 = 8 cm.

Answer: the height drawn from the top of the right angle is 8 cm.