# The height BM of triangle ABC divides its side AC into segments AM and CM. Find the length

September 27, 2021 | education

| **The height BM of triangle ABC divides its side AC into segments AM and CM. Find the length of the segment CM, if AB = 12√3, BC = 20 cm, angle A = 45 degrees.**

1. We calculate the length of the BM height through the sine ∠A = 90 °. Sine ∠A is the quotient of dividing the height of the BM, which in a right-angled triangle ABM is a leg by the length of the hypotenuse AB.

BM: AB = sine ∠A = sine 45 ° = √2 / 2.

BM = AB x √2 / 2 = 12√2 x √2 / 2 = 12 centimeters.

2. We calculate the length of the required segment SM (by the Pythagorean theorem):

CM = √BC²- BM² = √20²- 12² = √400 – 144 = √256 = 16 centimeters.

Answer: The length of the CM segment is 16 centimeters.

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