Math CentralQuandaries & Queries


Question from benny, a student:

Debby and john are looking up at their house from the backyard. From Debby's
point of view, the top of the house is at an angle of elevation of 40 degrees
From Johns point of view, directly closer to the house, it is 60 degrees. The
house is 15m high. How far apart are the two girls?

Girls? I know Martin Mull wrote a parody of Shel Silverstein's song "A Boy Named Sue" called "A Girl Named Johnny Cash", but...

Anyhow, start by drawing a diagram. It should show the top of the house, the point at ground level immediately below it, and the locations of Debby and John. If the problem is to have a solution, we must assume Debbie, John, and the bottom of the house to be on the same level.

Note that the point immediately below the top of the house is not mentioned anywhere in the problem. However, it is usually useful to add points like this that are implicit in vertically or horizontally measured distances.

Now you should be able to label three angles: the two given in the problems and the right angle at the foot of the perpendicular from the top of the house. You should also be able to label one edge length.

Now use trigonometry to add more labels to the diagram. If you get enough you will be able to answer your question. Careful planning should allow you to avoid finding things you do NOT need.

Good Hunting!

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