Help please
A flat roof has an inclination of 30 degrees to the floor of a building. The roof is square, 20m long (being parallel to the floor, 20m wide. Find the area of the projection of roof upon the floor of the building.
1. Draw a rough sketch (see attachment)
2. In the right triangle the width of the floor is the adjacent leg of the angle of 30°.
3. Let l denote the length of the square side. Then the area of the projektion of the roof upon the floor is:
$\displaystyle a = l \cdot l\cdot \cos(30^\circ)$
With $\displaystyle \cos(30^\circ) = \frac12 \cdot \sqrt{3}$ the area becomes:
$\displaystyle a=\frac12\cdot l^2 \cdot \sqrt{3}$
I dont get it. What is the value of L? I think its harder for me to visualize the image because it has been thought to us differently. Something like the one I attached. Can you explain it with my illustration? (illustration is bad, can someone fix it with the same idea, I just dont know where to put 30 degrees)
That's essentially the same picture earboth showed (except that his is larger and clearer!). The point is that the sloping surface makes an angle of 30 degrees with any horizontal line (such as the floor) and so makes a right triangle with hypotenuse of 20 m and angle 30 degrees.
The base leg, the projection onto the floor and the "near side" in the triangle, has length 20 cos(30). The other length is parallel to the floor and so its projection onto the floor is 20. the projection onto the floor is a rectangle with length 20 cos(30) and width 20 so its area is (20)(20 cos(30)), exactly earboth's formula.