Estimate the height of the tree...

Question

A forester, 175 feet from the base of a redwood tree, observes that the angle between the ground and the top of the tree is 60°. Estimate the height of the tree. (Round your answer to one decimal place.)

 

 

__?__ft.

Answer 1

We have the distance from the base of a tree on the ground to be 175 ft. To the top of the tree from that point it is 60º.  Can you tell what the angles are in the triangle?

The angle formed by the line to the point 175 feet away and the tree itself is 90 degrees. 60+90+x = 180

 

The Law of Sines tells us:

sin α = sin β
   a          b

Let a = the unknown height of the tree; b = 175 ft

Alpha = 60º; beta = 30º

 

sin(60º) = sin(?º)
    a              ?

 

It is not part of the problem, but try to see how far it is to the top of the tree from the point 175 ft. on the ground away from the base of the tree.