In a right-angled triangle ABC, the height BH drawn from the apex of the straight line of angle B
| April 12, 2021 | education
In a right-angled triangle ABC, the height BH, drawn from the top of the straight line of angle B, divides the hypotenuse into two segments AH = 36 cm and CH = 25 cm. Find: BH, AB, BC.
Since BH is the height that is lowered from the vertex of the right angle to the hypotenuse, then its length will be equal to:
BH = √ (AH * BH) = √36 * 25 = √900.
BH = 30 cm.
In a right-angled triangle ABН, we determine the length of the hypotenuse AB.
AB ^ 2 = AH ^ 2 + BH ^ 2 = 1296 + 900 = 2196.
AB = 6 * √61 cm.
In a right-angled triangle BCB, we determine the length of the hypotenuse BC.
BC ^ 2 = CH ^ 2 + BH ^ 2 = 625 + 900 = 1525.
BC = 5 * √61 cm.
Answer: The ВН height is 30 cm, the AB leg is 6 * √61 cm, the BC leg is 5 * √61 cm.
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