# The height CD of right-angled triangle ABC, drawn from the vertex of the right angle, divides the hypotenuse

The height CD of right-angled triangle ABC, drawn from the vertex of the right angle, divides the hypotenuse AB into segments AD and DB. Find the CD height if AD = 9cm, BD = 16cm.

Let the value of the angle ABC of the triangle DBC = X0, then the value of the angle DAC = (90 – X) 0.

In a right-angled triangle ACD, the angle ACD = (180 – ADC – CAD) = (180 – 90 – (90 – X)) = X0.

Then the angle ВDC = АСD, and therefore the right-angled triangles ВСD and АСD are similar in acute angle.

Then in similar triangles ACD and BCD:

AD / CD = CD / BD.

CD ^ 2 = AD * BD = 9 * 16 = 144.

СD = 12 cm.

Answer: The length of the height CD is 12 cm.

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