Find the height AN of triangle ABC if AC = 7 and AM = BM = 4.

univerkov | August 17, 2021 | education

Determine the length of the segment CM.

CM = AC – AM = 7 – 4 = 3 cm.

In a right-angled triangle BCM, according to the Pythagorean theorem, BC ^ 2 = BM ^ 2 + CM ^ 2 = 16 + 9 = 25.

BC = 5 cm.

Determine the area of the triangle ABC.

Savs = AC * BM / 2 = 7 * 4/2 = 14 cm2.

Also Savs = BC * AН / 2.

AH = 2 * Savs / BC = 2 * 14/5 = 5.6 cm.

Answer: The length of the height AH is 5.6 cm.

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