# In a right-angled triangle, one of the legs is 15 cm, the second 20 cm.

In a right-angled triangle, one of the legs is 15 cm, the second 20 cm. Find the height dropped from the top of the right angle to the hypotenuse.

1. A, B, C – the vertices of the triangle. S – area. AC = 20 centimeters. BC = 15 centimeters.

CE – height. ∠С = 90 °.

2. AB = √AC² + BC² (by the Pythagorean theorem).

BC = √20² + 15² = √400 + 225 = √625 = 25 centimeters.

3. S = AC x BC / 2 = 20 x 15/2 = 300: 2 = 150 centimeters².

4. We calculate the length of the height CE, using another formula for calculating the S triangle ABC:

S = AB x CE / 2.

CE = 2S: AB = 2 x 150: 25 = 300: 25 = 12 centimeters.

Answer: The length of the CE height is 12 centimeters.

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