How to find the height of a tree if you know the angle of elevation and your distance from the tree?

Question

State your distance from the tree and the measure of elevation, and calculate the height of the tree.

Answer 1

Just do the drawing, it would definitely help. 

 

The distance between you and the tree would be the base of a triangle, the height of the tree would be the height of a triangle, (and of course a line passing through where you are standing on the ground and the top of the tree would be the hypotenuse).

 

Since we are given the angle, we can use tan since tan (theta) is equal to opposite side (which we do not have, but want to find) over adjacent side which we have.

 

So:

 

tan(theta) =  opposite/adjacent

 

let's say theta was 60 degrees, and your distance to the tree was 50 meters.

 

Then:

 

tan(60) = X/ 50  => X= 50 * tan(60) = 50 * sqrt(3)                    where sqrt(3) means square root of 3