In a right-angled triangle ABC, the height drawn from the vertex of the right angle C to the hypotenuse is 6.
| July 4, 2021 | education
In a right-angled triangle BCH, we determine the length of the BH leg.
tgCBH = CH / BH.
√3 = 6 / BH.
BH = 6 / √3 = 2 * √3 cm.
The height drawn from the vertex of the right angle is equal to the square root of the product of the lengths of the segments by which the height divides the hypotenuse.
CH = √ (BH * AH).
CH ^ 2 = BH * AH.
36 = 2 * √3 * AH.
AH = 36/2 * √3 = 6 * √3 cm.
AB = AH + BH = 6 * √3 + 2 * √3 = 8 * √3 cm.
Answer: The length of the hypotenuse is 8 * √3 cm.
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