I am confused: 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)
The shade will be two m wide still.
However the shadow of the top will be 2 cos 60 from the shadow of the bottom.
To find the area of the shade that the students have to sit in, we need to find the projection of the shade onto the ground. We can do this by determining the length and width of the shadow.
Given that the shade is 1.5 m tall and makes an angle of 60° with the ground, we can use trigonometry to find the length of the shadow.
First, we need to find the length of the shade. Using the trigonometric function tangent, we can set up the equation:
tan(60°) = length of shade / height of shade
tan(60°) = length of shade / 1.5
To solve for the length of the shade, we can multiply both sides by 1.5:
1.5 * tan(60°) = length of shade
length of shade ≈ 1.73 m
Now that we know the length of the shade, we can determine the width of the shadow.
The width of the shadow is simply the width of the shade, which is 2 m.
Now, we can calculate the area of the shadow by multiplying the length and width:
Area of the shadow = length of shade * width of shadow
Area of the shadow ≈ 1.73 m * 2 m
Area of the shadow ≈ 3.46 square meters
Therefore, the area of the shade that the students have to sit in at 12 noon is approximately 3.46 square meters.