Basic Trigonometry
A person, standing on the bank of a river, observes that the angle subtended by a tree on the opposite bank is ; when he retires from the bank he finds the angle to be .Find the height of the tree.
The answer is 17.32.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Let H be the height of the tree, and x = the length of the river. We find:
tan(60 degrees) = H / x, which implies:
x = H/sqrt(3).
Further, tan(30 degrees) = H / (x + 20), which implies:
1/sqrt(3) = H / (H/sqrt(3) + 20).
Solving for H gives H = 10*sqrt(3)