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

May 31, 2020 | Education

| Denote the key points of the triangle as shown.

First, we find the hypotenuse of a right triangle ABC by the Pythagorean theorem:

AB2 = AC2 + BC2

AB ^ 2 = 120 ^ 2 + 35 ^ 2

AB ^ 2 = 14400 + 1225 = 15625

AB = 125

Consider the triangles ACD and ABC.

∠ADC is a straight line, since AD is the height and therefore equal to the right angle of the ACB.

∠CAD is common to these triangles.

Therefore, by the first sign, the triangles ABC and ACD are similar.

So we can write the proportion:

AC / AB = CD / CB

120/125 = CD / 35

CD = (120 * 35) / 125 = (120 * 7) / 25 = (24 * 7) / 5 = 33.6

Answer: 33.6

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