The legs of a right-angled triangle are 6 cm and 8 cm. Calculate the height drawn to the hypotenuse.

univerkov | May 9, 2021 | education

1. Vertices of the triangle – A, B, C. ∠C = 90 °. BC = 6 centimeters. CE – height. BC = 6 centimeters. AC = 8 centimeters.

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

AB = √BC² + AC² = √6² + 8² = √100 = 10 centimeters.

3. Calculate the area ΔАВС (S):

S = BC x AC / 2 = 6 x 8/2 = 24 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 24/10 = 4.8 centimeters.

Answer: The length of the CE height is 4.8 centimeters.

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