# In triangle ABC, angle C = 90, CH- height AB = 24, tgA = 1/7. find BH

August 24, 2021 | education

| Let’s use the definition of tangent and write down the ratio:

Tg A = BC / AC = 1/7.

Let’s define that the leg BC is equal to x, then AC is equal to 7x.

Let’s write down the Pythagorean theorem for a given triangle and find the square of the leg BC.

AB² = BC² + AC²

24² = x² + 49x²

50x² = 576

x² = 11.52

Knowing that the leg in a right-angled triangle is the average proportional between the hypotenuse and its projection onto the hypotenuse, we write:

ВС² = AB * BH, hence

BH = BC² / AB = 11.52 / 24 = 0.48.

Answer: the BH segment is equal to 0.48.

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