In triangle ABC, angle C is 90 degrees, bc = 12, cos A = 0.25. find the height CH.

In triangle ABC it is known:

Angle C = 90 °;

Leg bc = 12;

cos a = 0.25.

Find the height CH.

Decision:

1) sin a = √ (1 – cos ^ 2 a = √ (1 – 0.25 ^ 2) = √ (1 – (1/4) ^ 2) = √ (1 – 1/16) = √ (16/16 – 1/16) = √ (15/16) = √15 / 4;

2) sin a = BC / AB;

Hence AB = BC / sin a;

Substitute the known values into the formula.

AB = 12 / (√15 / 4) = 12 * 4 / √15 = 48 / √15;

3) sin B = CH / BC;

CH = BC * sin B;

Since cos A = sin B, then sin B = 0.25;

CH = 12 * 0.25 = 12 * 1/4 = 12/4 = 3;

As a result, we got that the height of a right-angled triangle is 3.

Answer: CH = 3.