Solving Triangles by Reflection

This is surprisingly easy to solve by using Reflection

Here is the triangle with its reflection

Together they make an equilateral triangle (all sides equal).

The angles in an equilateral triangle are all 60°

So the angle between the ladder and the wall is half of 60°

= 30°

Finding Length

We can use the same idea to find an unknown length.

Alex has a laser that measures distance.

By standing some distance from the tree Alex measures 42m to the top of the tree at an angle of 30°.

What is the height of the tree?

Here is the triangle and its reflection:

Once again the triangle and its reflection make an equilateral triangle.

So, we know the height of the tree must be half of 42m

= 21m

In fact reflection can help in many cases!