# Through the vertex C of the right-angled triangle ABC (angle C = 90 degrees), the perpendicular KS

Through the vertex C of the right-angled triangle ABC (angle C = 90 degrees), the perpendicular KC is drawn to its plane. Find the length of the AC leg if AB = 15 cm, KC = 5 cm, KB = 13 cm.

According to the condition CK, the perpendicular to the plane of the triangle ABC means that the triangle KCB is rectangular and the angle C is straight.

Let us define by the Pythagorean theorem the leg CВ of the triangle КCВ.

CB ^ 2 = BK ^ 2 – CK ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144.

CB = 12 cm.

Consider a right-angled triangle ABC, in which the hypotenuse AB = 15 cm and the leg CB = 12 cm.

Then, according to the Pythagorean theorem, the leg AC will be equal to:

AC ^ 2 = AB ^ 2 – BC ^ 2 = 15 ^ 2 – 12 ^ 2 = 225 – 144 = 81.

AC = 9 cm.

Answer: The length of the AC leg = 9 cm.

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