Find the height of a right-angled triangle from the vertex of the right angle if it divides
September 24, 2021 | education
| Find the height of a right-angled triangle from the vertex of the right angle if it divides the hypotenuse into 4cm and 16cm lengths.
In a right-angled triangle AB and AC – legs, BC – hypotenuse, AH – height.
BH = 4 cm; CH = 16 cm;
By the Pythagorean theorem
from tr – ka ABC: BC² = AB² + AC²;
from tr – ka AVN: AB² = BH² + AH²;
from tr – ka АСН: АС² = АН² + CH²;
Of the two last. express .:
AB² + BC² = BH² + AH² + AH² + HC²; AB² + BC² = 2 * AH² + BH² + CH²;
2 * AH² = (AB² + BC²) – BH² – CH²;
AB² + BC² = (BH + CH) ² = (4 + 16) ² = 400 (cm²);
BH² = 4² = 16 (cm²); CH² = 16² = 256 (cm²);
2 * AH² = 400 – 16 – 256 = 128 (cm); AH² = 64 cm²;
AH = √64 = 8 (cm).
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