In a right-angled triangle ABC (c = 90 °) the height CH is drawn. Find CH Ab = 25, sinA = 0.8.

univerkov | April 29, 2021 | education

Determine the cosine of the angle ACB.

Cos2ACB = 1 – Sin2ACB = 1 – 0.64 = 0.36.

CosACB = 0.6.

Then AC = AB * CosACB = 25 * 0.6 = 15 cm.

The ABC area is equal to: Saavs = AC * AB * SinCAB / 2 = 15 * 25 * 0.8 / 2 = 150 cm2.

Also Savs = CH * AB / 2.

CH = 2 * Savs / 2 = 2 * 150/25 = 12 cm.

Answer: The length of the CH height is 12 cm.

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