How to Find the Height of a 45-Degree Triangle with Given Base Segments

To find the height AD of triangle ABC, we can use trigonometry.

Let's start by drawing the triangle ABC with angle A at 45 degrees:

    B
   /|
  / |

6 / | x / | / | /_____
A 4 C

Given that BD = 6 and CD = 4, we want to find AD.

To find AD, we can use the tangent of angle A:

tangent(A) = opposite/adjacent

In this case, the opposite side is AD and the adjacent side is BD.

tangent(45) = AD/6

Since tangent(45) equals 1, we have:

1 = AD/6

Solving for AD:

AD = 6 * 1

AD = 6

Therefore, the height AD of triangle ABC is 6.