# The legs of a right-angled triangle are 35 and 120. Find the height drawn to the hypotenuse.

June 28, 2021 | education

| 1. Vertices of the triangle – A, B, C. Angle A – straight line. AE – height. S – area. The lengths of the legs AB and AC are 35 and 120 units of measurement, respectively.

2. AB² + AC² = BC² (along the tower of Pythagoras).

BC = √AB² + AC² = √35² + 120² = √1225 + 14400 = √15625 = 125 units.

3. S = AC x AB / 2 = 120 x 35: 2 = 2100 units of measurement².

4. Calculate the length of the height AE using a different formula for calculating S:

S = BC x AE / 2.

AE = 2 x 2100: 125 = 33.6 units.

Answer: height AE = 33.6 units.

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