In a right-angled triangle ABC, the length of the leg BC is 13 cm, and the height CD, drawn to the hypotinus AB

| July 18, 2021 | education

In a right-angled triangle ABC, the length of the leg BC is 13 cm, and the height CD, drawn to the hypotinus AB, is 12 cm. Calculate the length of the Projection of the leg BC onto the hypotenuse and the length of the leg AC.

Since CD is the height of the ABC triangle, the BCD triangle is rectangular.

Then, by the Pythagorean theorem, BD ^ 2 = BC ^ 2 – CD ^ 2 = 169 – 144 = 25.

ВD = 5 cm.

The height CD is drawn from the top of the right angle to the hypotenuse, then CD ^ 2 = BD * AD.

AD = CD ^ 2 / BD = 144/5 = 28.8 cm.

In a right-angled triangle ACD, according to the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = CD ^ 2 + AD ^ 2 = 144 + 829.44 = 973.44.

AC = 31.2 cm.

Answer: The length of the AC leg is 31.2 cm, the length of the segment BD is 5 cm.



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