A triangle with sides of 16 and 8 cm has heights drawn to these sides.

A triangle with sides of 16 and 8 cm has heights drawn to these sides. The height drawn to the 16 cm side is 6 cm.What is the height drawn to the 8 cm side

Given:
Δ ABC;
AB = 16 cm;
| CH = 6 cm;
BC = 8 cm;
| AN =?
To calculate the height drawn to the side, which is 8 cm, use the area of the triangle.
S = (a • h) / 2, where
a – side of the triangle;
h – height, lowered to this side;
S = (AB • CH) / 2;
S = (16 • 6) / 2 = 96/2 = 48.
To calculate the altitude AN, lowered to the side of the aircraft, you need:
h = (2 • S) / a;
h = (2 • S) / BC;
h = (2 • 48) / 8 = 96/8 = 12.
Answer: height AN = 12 cm.