In a triangle with sides 10 and 8, heights are drawn to these sides.

In a triangle with sides 10 and 8, heights are drawn to these sides. The height drawn to the second side is 5. Find the height drawn to the first side.

Given:

triangle ABC,

AC = 10,

BC = 8,

AN and BE heights,

AH = 5.

Find: the length of the height drawn to the side of the AC, that is, VK -?

Solution:

Consider triangle ABC. Let’s find its area (this is the product of 1/2 by the side and by the height drawn to this side):

S = 1/2 * AH * BC;

S = 1/2 * 5 * 8 = 4 * 5 = 20.

Then S = 1/2 * BK * AC;

S = 1/2 * BK * 10;

20 = 5 * BK

(in order to find an unknown factor, you need to divide the product by a known factor);

BK = 20: 5;

BK = 4.

Answer: 4.