In triangle ABC, angle C = 90, CH-height, AC = 3, cosA = 1/6. Find BH.

In a right-angled triangle ABC, knowing the length of the leg AC adjacent to the corner of BAC and the cosine of the angle BAC, we determine the length of the hypotenuse AB.

CosBAC = AC / AB.

AB = AC / CosBAC = 3 / (1/6) = 18 cm.

Let us consider the triangle ACН, which is rectangular, since CH is the height of the triangle ABC, and define through its hypotenuse AC the leg AH adjacent to the corner BAC.

CosВАС = АН / АС.

AH = AC * CosBAC = 18 * 1/6 = 3 cm.

Then the length of the sought segment BH will be equal to: BH = AB – AH = 18 – 3 = 15 cm.

Answer: The length of the VN segment is 16 cm.

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