Finding Length DB in a Complex Triangle Configuration: 6-Unit Height Problem

Question

Given the triangles in the drawing

What is the length of the side DB?

00:00 Find DB

00:03 We'll use the Pythagorean theorem in triangle ABC

00:12 We'll substitute appropriate values and solve for BC

00:22 Isolate BC

00:30 This is the length of side BC

00:33 Now we'll use the Pythagorean theorem in triangle BCD

00:43 We'll substitute appropriate values and solve for BD

00:49 Isolate BD

00:56 And this is the solution to the problem

In this question, we will have to use the Pythagorean theorem twice.

A²+B²=C²

Let's start by finding side CB:

6²+CB²=(2√11)²

36+CB²=4*11

CB²=44-36

CB²=8

CB=√8

We will use the exact same way to find side DB:

2²+DB²=(√8)²

4+CB²=8

CB²=8-4

CB²=4

CB=√4=2

2 cm