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° 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)

I did this: a b cos60/^2 and then multiplied the whole thing by 2 (because it is b) I wound up with an answer of 0.75. Is this correct?

I don't understand your logic. The projection of the area on the ground is ab*cos60, which is not .75m^2

My logic was this, as stated from a text book, which also showed your way: the projection of vector a onto b is found by (magnitude a)(magnitude b)(vector b) all over (magnitude b)2

This is not a projection of a vector, it is a projection of area.

To find the area of shade that the students have to sit in, you need to calculate the projection of the shade onto the ground. You were on the right track, but let me guide you through the correct calculations.

First, let's determine the length of the shade that is projected onto the ground. This length is the base of the shaded area.

To find the base, we can use the formula:

base = width × cos(angle)

In this case, the width is given as 2 m and the angle is 60°. So, substituting the values:

base = 2 × cos(60°)
base = 2 × 0.5
base = 1 m

Now we have the length of the base of the shaded area as 1 m.

Next, let's find the height of the shaded area. The height is the same as the height of the shade itself, which is given as 1.5 m.

So, the area of the shaded region is:

area = base × height
area = 1 × 1.5
area = 1.5 m^2

Therefore, the correct answer is 1.5 square meters, not 0.75 as you calculated.