Problem #10: Beth Koebel forgot her laser and discovers she has only a clinometer and tape with her. In addition, the trunk of the tree she wishes to measure cannot be reached. A large, nasty dog stands in front of the tree, zealously guarding it. However, there is a stretch of relatively level ground well in front of the tree and Beth finds that she can line herself up with the trunk and high point. How can Beth measure the height of the tree above eye level if she is able to see the top of the tree from the start and end of the level area?
Solution: The definitions, diagram, and formula below show how Beth can measure the height of the tree by using two vantage points P_{1} and P_{2} that are on the same level..
Definitions 





a =angle to crown from point P_{1} 



b =angle to crown from point P_{2} 



d = distance between points P_{1} and P_{2} 


h = height of tree above eye level 






Summary Comments: This method of measuring tree height is not typically presented in descriptions of height measuring. If d is too short, the error introduced by this method can be unacceptably large. Consequently, A d value of 20 feet should be the minimum. A d value of 30 feet would be safer. A future problem will address the magnitude of the error that can be expected from too short of a baseline.