In triangle ABC, angle C is 90 degrees, leg BC = 6, height CD = 4.8. Find the leg length AC.

In triangle ABC it is known:

Angle C = 90 °;

Leg BC = 6;

CD height = 4.8.

Find the leg length AC.

Decision:

1) The height CD of a right triangle is perpendicular to side AB.

Consider triangle ADB, with right angle D.

If the adjacent leg and the hypotenuse of a right triangle are known, then we can find the tangent of the angle between the sides.

sin B = CD / BC = 4.8 / 6 = 48/60 = 8/10 = 4/5 = 0.8;

2) cos B = √ (1 – sin ^ 2 B) = √ (1 – 0.8 ^ 2) = √ (1 – 0.64) = √0.36 = 0.6;

3) tg B = sin B / cos B = 0.8 / 0.6 = 8/6 = 4/3;

4) tg B = AC / BC;

AC = BC * tg A = 6 * 4/3 = 6/3 * 4 = 2 * 4 = 8;

Answer: AC = 8.