The height of a right-angled triangle drawn from the top of the right angle is 48 cm and the projection

univerkov | April 3, 2021 | education

The height of a right-angled triangle drawn from the top of the right angle is 48 cm and the projection of one of the legs onto the hypotenuse is 36 cm. Find the sides of this triangle.

1. A, B, C – the vertices of the triangle. ∠С = 90 °. CE – height. Segment BE = 36 cm.

2. We calculate the length of the segment AE, applying the formula for calculating the length of the height CE:

CE = √AE x BE.

CE² = AE x BE.

AE = CE²: BE = 2304: 36 = 64 cm.

3. BC = √CE² + BE² = √48² + 36² = √2304 + 1296 = √3600 = 60 cm.

4. AC = √CE² + AE² = √48² + 64² = √2304 + 4096 = √6400 = 80 cm.

5.AB = AE + BE = 64 + 36 = 100 cm.

Answer: BC = 60 cm, AC = 80 cm, AB = 100 cm.

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