Finding a tall tower's height

[psi20]

Hey, in our physics class, we're using lasers for an application of trigonometry. Anyways, today we were supposed to find out the height of a tower at our school. I thought we would be using lasers to figure it out, but we won't.

 

To do it, I believe you need a side and an angle.

 

My friend says to use a straw and look through it as a telescope to aim it at the top of the tower while you're close to the ground, then measure the angle. Then measure the distance you are from the tower and that should be enough to figure out the height.

 

This method would give a relatively accurate measurement since the tower is pretty tall.

 

But is there some other way to do it that would be less error-prone? Using the straw to look through it would be hard to do close to the ground and it would be easily blown away by the wind now.

[-Demosthenes-]

I don't think there is another way to measure the angle other then somehting very similar to that. It should be pretty easy provided that you know the trig.

[ydoaPs]

you'll need to know your height fairly accurately if it has to be as accurate as possible.

[psi20]

Ah, speaking of trig,

 

sin c * cos c = -.5

 

Is it possible to find out c?

[psi20]

Another way might be, assuming that the ground that the tower's shadow goes onto is flat, to walk along the shadow until the shadow hits the top of your head. Then use your height, the total length of the shadow, and the total length of the shadow - distance you walked to find the height of the shadow.

[ydoaPs]

don't you still need an angle?

[psi20]

I don't think so, just use triangle similarity properties.

 

Using the top of the tower, the point where the tower meets the ground, and the end of the tower's shadow, we have triangle ABC. I walk a distance until the tower's shadow hits the top of my head. Using the top of my head, the point where my foot meets the ground, and the end of the tower's shadow, we have triangle DEC.

 

These triangle are similar from because two angles are the same, one right angle and angle C.

AB/BC = DE/EC

 

Then you just find AB since you can measure the rest.

[ydoaPs]

o, ok. I just got confused on what you were saying. yea it would work.

 

[math]\frac{h}{L}=\frac{x}{l}[/math]

 

h is your height. L is the lenght of your shadow. l is the lenght of the building's shadow.

[Skye]

Usually you use a thing called a clinometer. You look through a little hole in it at what you are measuring and there's a little gauge that tells you the angle it's pointed at. You measure the angle to the top and bottom, bcause a) you aren't at ground level if you're standing, and b) the ground mightn't be level. The measure the distance to the base of the object and do the trig.

 

You could do this with a straw and a protractor though, just need to keep the protractor still while you measure the two angles.

[pulkit]

Ah' date=' speaking of trig,

 

sin c * cos c = -.5

 

Is it possible to find out c?[/quote']

 

Multiply equation by 2 to get Sin 2c = -1

Then you can use standard results to get your set of solutions

[ydoaPs]

Usually you use a thing called a clinometer. You look through a little hole in it at what you are measuring and there's a little gauge that tells you the angle it's pointed at. You measure the angle to the top and bottom' date=' bcause a) you aren't at ground level if you're standing, and b) the ground mightn't be level. The measure the distance to the base of the object and do the trig.

 

You could do this with a straw and a protractor though, just need to keep the protractor still while you measure the two angles.[/quote']

 

put a peice of string with a washer at one end on the center of the flat part of the protractor. tape the straw along the flat edge with the string so that the washer is on thew end away from the protractor.

[ydoaPs]

make sure the edge of the protractor is on the edge of the straw.