Sides AB and BC of triangle ABC are 16 cm and 22 cm, respectively, and the height drawn

Sides AB and BC of triangle ABC are 16 cm and 22 cm, respectively, and the height drawn to side AB is 11 cm. Find the height drawn to side BC.

Let the height drawn to the side AB intersect AB at the point M;

Triangle CMB rectangular with leg CM = 11, equal to half of the hypotenuse BC = 22;

Hence the angle MBC = 30 °;

Lower the height AN to the BC side;

In triangle ABN, leg AN lies opposite an angle of 30 ° and, therefore, is also equal to half of the hypotenuse AB;

AN = 16/2 = 8 cm.