In a right-angled triangle, one of the legs is 3 cm, and the hypotenuse is 5 cm.
| August 7, 2021 | education
In a right-angled triangle, one of the legs is 3 cm, and the hypotenuse is 5 cm.Find the other leg and the height attributed to the hypotenuse
1. A, B, C – the vertices of the triangle. S – area. CE – height. ∠С = 90 °. AC = 3 centimeters.
AB = 5 centimeters.
2. ВС = √АВ²-АС² (by the Pythagorean theorem).
BC = √5² – 3² = √16 = 4 centimeters.
3. S = AC x BC / 2 = 3 x 4/2 = 6 centimeters².
4. We calculate the length of the height CE, using another formula for calculating the area of a triangle:
S = AB x CE / 2.
CE = 2S: AB = 2 x 6: 5 = 2.4 centimeters.
Answer: the length of the BC leg is 4 centimeters, the length of the CE height is 2.4 centimeters.
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