The legs of a right-angled triangle are 1: 3. Find the height of a triangle dropped from the vertex of a right angle if the hypotenuse is 40
1. Vertices of the triangle – A, B, C. Angle A – straight line. AE – height. S – area. AB: AC = 1: 3.
BC = 40 units.
2. AC = 3AB.
3. AB² + AC² = BC² (along the tower of Pythagoras). We substitute 3AB here instead of AC:
AB² + (3AB) ² = 1600.
AB² + 9AB² = 1600.
AB² = 160.
AB = 4√10 units of measurement.
AC = 3 x 4√10 = 12√10 units of measurement.
4. S = AB x AC / 2 = 4√10 x 12√10 / 2 = 240 units.
5.S = BC x AE / 2.
AE = 2 x 240: 40 = 12 units.
Answer: AE height is 12 units.
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