The angle of elevation of the top of an unfinished tower at a point is 80 m from the base is 30 degrees.How much higher must be the tower to be raised so that its angle of elevation at the same point be 60 degrees?

Question

The angle of elevation of the top of an unfinished tower at a point is 80  m from the base is 30 degrees.How much higher must be the tower to be raised so that its angle of elevation at the same point be 60 degrees?

aaronandyson · Answer

@phi

anonymous · Answer

I'd just like to confirm, but the base length will not be changing right?

aaronandyson · Answer

I'm concerned about that also lol

aaronandyson · Answer

In all probability It shouldn't change.

anonymous · Answer

Because if it doesn't then I have it figured it out

aaronandyson · Answer

Help me then?

anonymous · Answer

Sure. The whole way of doing this problem goes on the basis of the properties of 30-60-90 triangles. The original triangle will have a base of $$80\sqrt{3}$$

aaronandyson · Answer

HA!
They had told to take sqrt3 as 1.73
I got the base length to be as 138.4m

anonymous · Answer

Well if you have a 30-60-90 triangle and the 30 degrees side is 80, the other side will just be that times sqrt3. You could write it as the decimal form but it's a lot neater otherwise. So we are going to have two pieces of info going into the second triangle. That the base is $$80\sqrt{3}$$ and that the new angle opposite the wall will be 60

anonymous · Answer

|dw:1431698120231:dw| Now just use the same properties of a 30-60-90 triangle with the base as the 30 now and the wall as the 60.