At what minimum height above ground level must I place a satellite dish so that at a 30-degree angle, it will be able to “see” the sky over the top of a building that is 40 feet tall and 50 feet away from the dish?

Question

tkhunny · Answer

Draw a right triangle with legs at the horizontal (longer leg) and the vertical (shorter leg).
Resist Labeling the vertical (part of the building), for now.
Label the horizontal (ground) 50 ft
Label the acute angle away from the building 30º.
Calculate the length of the short (vertical) side.

You're almost done.

anonymous · Answer

I calculated the length of the short side as 50(sqrt(3)/3). How do I find the minimum height?

tkhunny · Answer

$\dfrac{50}{\sqrt{3}}$ - Excellent!

You need this distance to end at the top of the building, rather than start at the bottom of the building.  Thus, you must raise your triangle $\left(40 - \dfrac{50}{\sqrt{3}}\right)\; ft$.  Personally, I would add one radius of the dish, but that's just me.

anonymous · Answer

ok, thank you!