The legs of a right-angled triangle are 3 cm and 4 cm. Calculate the height projected to the hypotenuse.

univerkov | May 9, 2021 | education

1. Vertices of the triangle – A, B, C. ∠C = 90 °. BC = 6 centimeters. CE – height. BC = 3 centimeters. AC = 4 centimeters.

2. Calculate the length of the hypotenuse AB using the Pythagorean theorem:

AB = √BC² + AC² = √3² + 4² = √25 = 5 centimeters.

3. Calculate the area ΔАВС (S):

S = BC x AC / 2 = 3 x 4/2 = 6 centimeters².

4. Calculate the length of the CE height using another formula S:

S = AB x CE / 2.

CE = 2 x S / AB = 2 x 6/5 = 2.4 centimeters.

Answer: The length of the CE height is 2.4 centimeters.

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