Ptolemy's Ptools

Measuring the Height of a Building or Tree

A good way to get familiar with your new tool is to measure the height of a building or tree.

Materials needed:

1) Quadrant

2) Measuring Tape (at least 10 meters long)

What to do:

Go outside and walk away from a building (or tree), pausing occasionally to sight the top with your quadrant.

Continue moving away from the building until you get an angle of 45° on the quadrant scale.

How It Works:

Recalling some properties of triangles , we can assume that

(a)all triangles have three angles that always add up to 180° and

(b)all ISOSCELES triangles (triangles with two equal angles) have two equal side lengths (and visa versa)

Picture a triangle with three corners at ---

(1) the top of the building,

(2) the bottom of the building and

(3) you.

We can estimate that the angle of the building to the ground is 90° . We know that another angle of our triangle is 45° because we measured it with our quadrant. That means that the other corner has to be 45° also(the angle at the top of the building).

We can deduce that we have an isosceles triangle, with equal length sides from us to the building and from the bottom to the top of the building. All we need to do is measure the distance back to the building and we will know its height.

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(last updated 8/31/98)