Two math students erect a sun shade on the beach.  The shade is 1.5 m tall, 2 m wide, and makes an angle of 60 degrees with the ground. What is the area of shade that the students have to sit in at 12 noon (that is, what is the projection of the shade onto the ground)? (Assume the sun's rays are shining directly down).

Expert Answers

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The shade is made of a piece of material that has a length of 1.5 m and a width of 2 m. It is placed at an angle of 60 degrees to the ground when the shade is created.

At 12 noon, when the sun is shining directly down only the component of the area of the material that is horizontal to the ground is going to provide protection to the students.

This area is 1.5* cos 60 * 2

=> 1.5* 0.5 * 2

=> 1.5 m^2

The required area that the students can sit in, at 12 noon, is 1.5 m^2.

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