# Solving Triangles by Reflection

A 5ft ladder leans against a wall as shown. What is the |

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 = 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!