## Imaginary Mountains (Laws of Sines and Cosines)

Sometimes when I try to follow my lesson plan trick of turning word problems into reality, I face the issue of not having an actual steamroller or orbiting satellite to play with. But with a little imagination I can fake it, and the students play along.

You are standing near a lake. From where you are standing it is 120 meters to one side of the lake and 140 meters to the other side. The angle between the sides of the lake from your vantage point is 94 degrees. Find the width of the lake.

You are on the ground trying to find out the highest point of a mountain. You find the angle you have to crane your neck at to look directly at the top of the mountain is 71 degrees. You walk forward 1000 meters and find the angle to the top of the mountain is now 83 degrees. How tall is the mountain?

Both are good enough problems with pre-manufactured numbers, but what if the students could do them with their own data? I don’t have any handy mountains or lakes to test on.

So we went out to the football bleachers and called the back wall a “lake” to do the first problem and a “mountain” to do the second. In reality the students could easily walk along the wall and get the measurement, but we were imagining a situation where that wasn’t possible, which was enough to convince students of a “real-life” purpose to the mathematics.