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A Bright Sunny Day

Module by: Interactive Mathematics Program

Intent

The mathematical work of the unit concludes with this activity, in which students put their knowledge of trigonometry to use to find the solution to the second part of the unit problem: finding a formula for the length of a sun shadow.

Mathematics

The length of a sun shadow is a function of two variables: the height of the object casting the shadow and the angle of elevation of the sun. The object, the shadow, and the line of sight to the sun create a right triangle. The length of the shadow can be found using trigonometry.

Progression

Students work on this final activity in groups and share their results as a class.

Approximate Time

25 minutes

Classroom Organization

Groups, followed by whole-class discussion

Doing the Activity

You may want to review the diagram in the student book with the class. You might suggest that groups start with specific values for H and θ, which may help them figure out how to solve the trigonometric equation for S in terms of H and θ.

If necessary, tell students that the angle of elevation from their eyes to the sun is the same as the angle in the triangle formed by their bodies and their shadows (both labeled θ in the diagram below).

Discussing and Debriefing the Activity

There are essentially three steps to solving this problem. You may want to have presentations on each.

  • Setting up a clear, correctly labeled diagram
  • Using the diagram to get an equation involving S, H, and θ
  • Solving this equation for S in terms of H and θ

Once students have a diagram like the one below, they will probably start with the equation tan=HStan=HS size 12{"tan"= { {H} over {S} } } {}, which they must then solve for S. It may help to work this out once or twice with specific values for H and θ and then use those examples to develop the general equation S=HtanS=Htan size 12{S= { {H} over {"tan"} } } {}.

Figure 1
Figure 1 (graphics1.jpg)

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