Suppose the billboard is 80 feet wide and stands 60 feet from the road, perpendicular to the road. We will call the distance you are from the billboard x and the viewing angle θ. 1. Draw a picture of this situation labeling the distances, x, and θ. 2. Make note of the two right triangles in the picture and the of the angles to θ. 3. Write an equation for θ in terms of x. 4. Find the rate of change of θ with respect to x 5. For what x value is the rate of change equal to 0? This is the location with the maximum viewing angle.

Question

Suppose the billboard is 80 feet wide and stands 60 feet from the road,
perpendicular to the road. We will call the distance you are from the
billboard x and the viewing angle θ.
1. Draw a picture of this situation labeling the distances, x, and θ.
2. Make note of the two right triangles in the picture and the of the angles
to θ.
3. Write an equation for θ in terms of x.
4. Find the rate of change of θ with respect to x

5. For what x value is the rate of change equal to 0? This is the location
with the maximum viewing angle.

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