The legs AC and BC of the right-angled triangle ABC are related as 3: 4, respectively.
| June 15, 2021 | education
The legs AC and BC of the right-angled triangle ABC are related as 3: 4, respectively. Find the height of a right-angled triangle from the vertex of the right angle if the hypotenuse is 20.
1. BE – height. S – area.
2. AB: BC = 3: 4. AB = 3BC / 4.
3. AB² + ВС² = АС² (along the tower of Pythagoras).
(3BC / 4) ² + BC² = 400.
9BC² / 16 + BC² = 400.
25BC² = 400 x 16.
ВС² = 256.
BC = 16 units.
AB = 3 x 16/4 = 12 units.
4. S = BC x AB / 2 = 12 x 16: 2 = 96 units².
5. We calculate the length of the height BE, using another formula for calculating S:
S = AC x BE / 2.
BE = 2 x 96: 20 = 9.6 units².
Answer: height BE = 9.6 units ².
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