Find the height dropped on the hypotenuse of a right-angled triangle if its legs are 3 cm and 5 cm.

1. A, B, C – the vertices of the triangle ∠C = 90 °. The lengths of the legs BC and AC are 3 centimeters and 5 centimeters, respectively. CE – height.

2. Calculate the length of the side AB (hypotenuse). For the calculation, we use the Pythagorean theorem:

AB = √BC² + AC² = √3² + 5² = √9 + 25 = √34 centimeters.

3. Calculate the area (S) of a given triangle:

S = BC x AC / 2 = 3 x 5 = 15/2 = 7.5 centimeters².

4. Find the length of the height CE. To do this, we use another formula for calculating the area:

S = AB x CE / 2.

CE = 2S / AB = 15 / √34 centimeters.

Answer: the length of the height CE = 15 / √34 centimeters.