Dylan is using his clinometer to help him determine the height of a tree. He stands 6 m from the base of the tree and takes the measurement shown on the clinometer. Then, he measures the height of his eye to be 1.6 m above the ground.
a. Sketch a diagram to represent this scenario.
I subtracted 90 from 42 (the angle on the clinometer above) and got 48 degrees as the other angle.
b. Determine the height of the tree.
tan = opposite / adjacent
a = tan a° x C (distance)
b = tan b° x C (distance)
Tree height = a + b
a = 6tan(42°) = 5.4024…
b = 6tan(48°) = 6.6636…
a + b = 12.0660…
The tree is 12 meters tall; did I do this correctly? Any help at all is appreciated, just be sure to be clear about it. Thanks!
Best Answer
Let me provide an alternate solution. The height of the tree is the height of the man plus the portion above the man. This portion has length 6tan(42 degrees), which is about 5.4 meters. Adding this to the man's height, we see that the height of the tree is about 7.0m. I don't think you can assume that the angle between the man's sightline of the top of the tree and the foot of the tree is 90 degrees - consider the extreme case of the man standing really far away from the tree. Hope this helps!