The height of the right-angled triangle is 6, and the projection of one of the legs is 12. Find the hypotenuse.
| July 23, 2021 | education
1. A, B, C – the vertices of the triangle. ∠С = 90 °. CE – height. Segment BE = 12 centimeters – projection of the BC leg onto AB.
2. We calculate the length of the segment AE, which is the projection of the leg AC on AB, using the formula for calculating the length of the height CE, which is drawn from the vertex of an angle equal to 90 °.
CE = √AE x BE.
CE² = AE x BE.
AE = CE²: BE = 36: 12 = 3 centimeters.
AB = AE + BE = 3 + 12 = 15 centimeters.
Answer: the length of the hypotenuse AB is 15 centimeters.
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