SOLUTION: the angle of elevation of the top of a tree from a point P is 7 degree. After walking 30m towards the tree, the angle of elevation becomes 9.1. Find the height of the 10?

Algebra ->  Points-lines-and-rays -> SOLUTION: the angle of elevation of the top of a tree from a point P is 7 degree. After walking 30m towards the tree, the angle of elevation becomes 9.1. Find the height of the 10?      Log On


   

Question 843492: the angle of elevation of the top of a tree from a point P is 7 degree. After walking 30m towards the tree, the angle of elevation becomes 9.1. Find the height of the 10?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Here is a sketch illustrating the problem:
To show those right triangles clearly, I had to draw the angles much wider than 7%5Eo and 9.1%5Eo .
The height of the tree is h .
After walking 30m towards the tree, at a distance d from the base of the tree, the angle of elevation becomes 9.1%5Eo and
tan%289.1%5Eo%29=h%2Fd<--->d%2Fh=1%2Ftan%289.1%5Eo%29
From point P, at a distance d%2B30m from the base of the tree, the angle of elevation was 9.1%5Eo and
tan%287%5Eo%29=h%2F%28d%2B30m%29<--->%28d%2B30m%29%2Fh=1%2Ftan%287%5Eo%29
%28d%2B30m%29%2Fh-d%2Fh=1%2Ftan%287%5Eo%29-1%2Ftan%289.1%5Eo%29
%28d%2B30m-d%29%2Fh=1%2Ftan%287%5Eo%29-1%2Ftan%289.1%5Eo%29
30m%2Fh=1%2Ftan%287%5Eo%29-1%2Ftan%289.1%5Eo%29
From now on we calculate approximate values, rounding as needed.
30m%2Fh=1%2F0.122785-1%2F0.160174
30m%2Fh=8.1443-1%2F6.2432
30m%2Fh=1.9011
30m%2F1.9011=h
h=highlight%2815.78m%29