Height of a tree (angle of elevation)

Question

Im trying to find the height of a tree and so far I have angle of elevation measured from a clinometer at: 155 degrees and a distance from the tree at: 4.2 metres. any help?

Answer 1

     The best I can figure is if you draw a diagram with the tree being the vertical segment, the distance on the ground from dinometer to the base of the tree,which is 4.2 meters, and an imaginary line from the clinometer to the tree top form a triangle. The angle of elevation is an acute angle formed by a horizontal line and the line of sight to the top of the tree. This is why I'm a little confused by the numbers in your problem. Your diagram should be a right triangle. This is why the angle of elevation cannot be 155. I'm guessing that maybe a clinometer measures the exterior angle which would make the interior angle of the triangle 35 degrees????

     Assuming this is correct, you are looking for the height of the tree, call it x, and we know the ground distance of 4.2 meters. These segments are related to my angle of elevation. x is opposite and 4.2 is adjacent. This tells me that the problem must deal with tangent. So,

 

tan 35 = x/4.2

.700207538 = x/4.2 

.700207538 * 4.2 = x

2.94087166 = x

 

Since the problem doesn't tell me what decimal place I should round off to, I would leave my answer of 2.94087166, the most accurate answer I can find.

Hope this helps.