two math students erect a sun shade on the beach (similar to the one pictured here). the fabric of the shade is 1.5 m long (from the ground to the top) and 2 m wide, and the students erect it so it makes an angle of 60° 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)

Work Shown:

The portion of the fabric that is laying across the ground is 2 meters. The portion of the fabric from the ground to the highest point (along the fabric's edge) is 1.5 meters, half of that is 0.75 meters and this is the length of the shadow. We can see this by forming a 30-60-90 triangle. The hypotenuse is 1.5 meters, the short leg is 0.75 meters. The short leg is always half of the hypotenuse of any 30-60-90 triangle, and the short leg is opposite the 30 degree angle.

So this shadow has length of 2 meters and 0.75 meters, making its area be 0.75*2 = 1.5 square meters when the sun is directly overhead at 12 noon