# Distance Off by Similar Triangles

When two triangles have internal angles of the same value they are called similar. One characteristic of similar triangles is that although their sides have different lengths, they are proportionate to each other. The ratio of any two sides in the first triangle equals the ratio of the same sides in the second triangle. If you know the length of any three of these four sides, finding the value of the fourth is straightforward.

You would like to know the distance between you and the lighthouse of a known height. Hold a ruler at arm's length (57 centimetres) and measure the height of the lighthouse on the ruler in centimetres. You now know three of your four sides and can calculate the distance off (illustrated in Figure 12.3).

Triangle ABC and ADE are similar so their sides are proportionate to each other. This means:

1. AE which is your hand to eye distance

2. DE which is the height on your ruler

3. BC which is the height of the feature

You want to know the distance off which is AE and the equation is rearranged as:

AB = BC x AE / DE AE = 41 x 0.57 / 0.04 Distance Off = AE = 5842m

Triangle ABC and ADE are similar so their sides are proportionate to each other. This means:

1. AE which is your hand to eye distance

2. DE which is the height on your ruler

3. BC which is the height of the feature

You want to know the distance off which is AE and the equation is rearranged as:

AB = BC x AE / DE AE = 41 x 0.57 / 0.04 Distance Off = AE = 5842m

There are 1-852m in a nautical mile so you are 3.2nm off the light. 12.3 Distance Off by Similar Triangles

There are 1-852m in a nautical mile so you are 3.2nm off the light.

12.3 Distance Off by Similar Triangles