In triangle ABC, angle C is 90, CH-height, BC = 16, sinA = 0.25. Find BH.
| August 14, 2021 | education
In a right-angled triangle, the sine of the angle is equal to the ratio of the opposite leg to the hypotenuse. Means,
sin A = BC / AB.
From here
AB = BC / sin A.
Find the hypotenuse AB:
AB = 16 / 0.25 = 64.
Consider a triangle BCH. It is rectangular with right angle H. Angle BCH is equal to angle A of triangle ABC. This means that their sines are equal, that is,
sin BCH = 0.25.
The BH side can be found from the expression
BH = sin BCH * BC.
Find BH:
BH = 0.25 * 16 = 4.
Answer: BH = 4.
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