In a triangle with sides 15 and 3, heights are drawn to these sides. The height drawn to the first side is 1.

In a triangle with sides 15 and 3, heights are drawn to these sides. The height drawn to the first side is 1. What is the height drawn to the second side?

The area of a triangle is calculated by the formula S = (a * h): 2.

1 way

Consider the triangle ABC. S = (a * ha): 2 = 15 * 1: 2 = 7, 5.
Consider the triangle ABC. S = (b * hb): 2,
hb = 2 * S: b,
hb = 2 * 7.5: 3,
hb = 5.

2 way

Consider the triangle ABC. S = (a * ha): 2.
Consider the triangle ABC. S = (b * hb): 2.
We are considering the same triangle, therefore, their areas are equal.
(a * ha): 2 = (b * hb): 2.
Substituting numerical values and solving the equation, we will find the answer to the question of the problem.
Answer: the height is 5.