# The legs of a right-angled triangle are 1: 3. Find the height of a triangle dropped from the vertex

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. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.