Three heights are drawn in the triangle, the largest of which is 8.

Three heights are drawn in the triangle, the largest of which is 8. Find the lower of the heights if the larger and smaller sides of the triangle are 10 and 6.

It is known that in a triangle a lower height is drawn to the larger side, and vice versa, a greater height is drawn to the smaller side. Therefore, to the side equal to 6, a height equal to 8. We can find the area of a given triangle as half the product of the length of the side and the height drawn to it:

S = 0.5 * 6 * 8 = 24.

Knowing that the large side is 10, we find the smaller height:

S = 0.5 * 10 * h;

h = 2 * S / 10 = 2 * 24/10 = 48/10 = 4.8.