Finding the height of a tree

• May 2nd 2009, 02:12 PM
tribalxgecko
Finding the height of a tree
I am working on my math homework and am completely stumped...maybe somebody can point me in the right direction?

Here is the question:

"Bob is looking at a bird's nest at the top of a very tall tree and wonders how high it is. From where he stands, he finds that the angle of elevation is 40.1 degrees. He then walks back 30 ft and finds the angle of elevation to be 35.5 degrees. Find the height of the tree."

What I can't figure out is how to do this without being give one of the sides. The only thing I could think of is to do Tan(36.5) = X / 30+Y. But that still does not let me do anything due to both variables.

Thanks for any help.(Doh)
• May 2nd 2009, 02:19 PM
VonNemo19
Let the distance he was initially away from the base of the tree be x

then tan41.1=o/x and tan35.5=o/(x+30)

solving for o in both equations yields

(tan41.1)(x)=o and (tan35.5)(x+30)=o

and since o=o

(tan41.1)(x)=(tan35.5)(x+30)

can you take it from here?
• May 2nd 2009, 02:22 PM
tribalxgecko
Yep, I can go from there, that is all I needed. Thank you very much!!
• May 2nd 2009, 02:24 PM
VonNemo19
no problemo kid!