We want to measure the height of a building based on the shadows and known height in the problem. Let's draw a diagram illustrating the telephone pole, the building, and the shadows.
Segment PR illustrates the telephone pole, and PQ is its shadow.
Segment BD illustrates the building, and BC is its shadow.
We are asked to find the height of the building, which is BD on our diagram.
The sun is very far away, so the rays that form the shadows of the telephone pole and building are parallel.
RQ∥ DC
Since both the telephone pole and the building stand on horizontal ground, and both the pole and the building stand vertically, the triangles are similar.
△ PQR~ △ BCD
In similar triangles, the length of corresponding sides are proportional.
DB/RP=BC/PQ
If we substitute the measures given on the diagram into this ratio, we can solve the resulting equation for the height of the tree.
