In triangle ABC, angle C = 90, AC = 5 cosA = 24/25 find the height CH.

In the ABC triangle it is known:

Angle C = 90 °;
AC = 5;
cos A = 24/25.
Find the height CH.

Decision:

1) Consider a triangle ACН with a right angle H.

Find sin a.

sin a = √ (1 – cos ^ 2 a) = √ (1 – (24/25) ^ 2) = √ (1 – 576/625) = √ (625 – 576) / √625 = √49 / √625 = 7/25;

Hence, sin a = 7/25.

2) sin a = CH / AC;

From here we express CH and calculate the value of the CH height.

CH = AC * sin a;

Plug in the known values and calculate the height value.

CH = 5 * 7/25 = 5/25 * 7 = 1/5 * 7 = 7/5 = 5/5 + 2/5 = 1 + 2/5 = 1 + 0.4 = 1.4.

Answer: CH = 1.4.