Calculating Shade Projection for Beach Sun Shade - Math Homework Solution

[unknown101]

Homework Statement

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).

Homework Equations

I've attached the formula

The Attempt at a Solution

I tried drawing a diagram with 2m at the bottom and the height being 1.5. I know I'm supposed to use the projection formula. After that I'm lost.

 

[The Bob]

Just for my own clarity, does it make a 60° angle with the bit that goes in the ground or with the actual shade itself? Could you produce a diagram if this seems to be a silly question?

The Bob

 

[unknown101]

With the piece that goes in the ground. The problem didn't come with a diagram because so you have to come up with your own.

 

[HallsofIvy]

60 degrees is an angle in an equilateral triangle. The edge of the shadow, with the sunlight coming straight down is at the perpendicular from the vertex. This is very close to being a trivial problem!

 

[hossai]

how would u solve this problem guys?

 

[The Bob]

how would u solve this problem guys?

Hi hossai. Welcome to PF!

The idea of these threads is to help each other solve problems they have. So, if you'd like to venutre an attempt at the solution or method for solving this then we could discuss it further.

The Bob