In triangle ABC, angle C is 90, CH-height, AB-27, cos A = 2/3. Find: BH-?

univerkov | February 18, 2021 | education

Consider a triangle ABC. cos A = AC / AB = 2/3. We express AC: AC = 2 * AB / 3.

Consider the triangle CHA. cos A = AH / AC = 2/3. We express AH: AH = 2 * AC / 3 = 2 * 2 * AB / (3 * 3) = 4 * AB / 9 = 4 * 27/9 = 12.

BH = AB – AH = 27 – 12 = 15.

In response, write BH = 15.

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