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

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
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}