Estimating the Height of a Building from Another Building?

you need an instrument (e.g. theodolite) to measure the angle subtended by the bottom and top of the building. once you know this angle and the horizontal distance between the building and you, you can use basic trignometric funtion like 'tan' to measure the height of the building.

yes, the same method can be used to estimate the height of the building when you standing on the ground.

if the building is very far to measure the horizontal distance from you. you can follow the above mentioned procedures at two different locations and by measuring the distance between these two locations ( e.g. 10 metres) and basic trignometric calculations you can find the height of the building.

edited after additional details:

angle subtended: imagine a line from the top of the building to the point where you are standing. imagine another line from the bottom of the building and the same point, so that it intersects. now the angle between these two lines is the angle subtended by the building. you can divide this angle into: angle between top of the building and the horizontal, say 'alpha'; and angle between bottom of the building and the horizontal, say 'beta'. if you can somehow find the distance between the other building and the point where you are standing (horizontal distance....you can use a tape to measure the distance between the base of the two buildings), then height of the building = horz. distance * (tan(alpha) + tan(beta))

note: horiz. distance * tan(alpha) gives height of the building above your level.

horiz. distance * tan(beta) gives height of the building below your level.

you just have to add these two values to get the total height.

you formula containing -ve sign is valid if you are considering angle beta as -ve, which will make -tan(beta) +ve.

if you dont have any instruments, the best you can do is measure the no. of floors and multiply it with the approximate height of each floor. also accounting for slab thickness.

the height of each story can in turn be measure by multiplying number of steps in the stair case and rise of each step. this is very easy to calculate and yields fairly accurate result. you don't have to account for roof thickness since it's already covered. of course, with an assumption that each story is of same height.

but, if you just want to measure the height of another building without any instruments, or knowing the horizontal distance, or having access to it's staircase, i am afraid there is no way of doing it.

Interesting.. is this a question you have an answer to already and are testing us? or do you want to know?

When you say you have no special equipment, what do you mean? Absolutely nothing? Do you have things like a tape measure, a stopwatch, a calculator?

You could drop something large off the building you are on and time its fall till the ground work out your height... repeat for better accuracy.

If you have a spirit level and a tape measure you can estimate the angle between horizontal at your position and the top of the opposite building relatively accurately.

Measuring the horizontal distance between you and the other building will be the most difficult. If the other building is taller and not too far away you could potentially create a loud noise and time until you hear the echo. then knowing the speed of sound in air you could get an estimate. from there you could calculate the height of the other building.

I think the easiest way would be to find a common object of known height next to a floor (eg a car on the street next to the building, a road sign, a computer in a window) then use this to estimate the height of a single floor. Then count the number of floors and multiply.. you'd have to estimate extras like the roof etc. Probably could get it suprisingly accurate as most skyscrapers are very regular buildings.. be a lot quicker too.