The legs of a right triangle are 16cm and 12cm. Find the height of a triangle from the vertex of a right angle.
| February 16, 2021 | education
1. Vertices of the triangle – A, B, C. Angle A – straight line. AE – height. S – area. Length of legs
AB and AC are 16 and 12 centimeters, respectively.
2. AB² + AC² = BC² (along the tower of Pythagoras).
BC = √AB² + AC² = √16² + 12² = √256 + 144 = √400 = 20 centimeters.
3. S = AC x AB / 2 = 16 x 12: 2 = 96 centimeters².
4. Calculate the length of the height AE using another formula for calculating S:
S = BC x AE / 2.
VK = 2 x 96: 20 = 9.6 centimeters.
Answer: height AE = 9.6 centimeters.
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