Thomas stood 12.0 m from the base of a tree. He used a clinometer to sight the top of the
tree. The angle shown on the clinometer was 70°. Thomas held the clinometer 2.2 m about the
ground. Determine the height of the tree to the nearest tenth of a metre.
Answers
Given : Thomas stood 12.0 m from the base of a tree.
He used a clinometer to sight the top of the tree.
The angle shown on the clinometer was 70°.
Thomas held the clinometer 2.2 m about the ground.
To Find : The height of the tree to the nearest tenth of a metre.
Solution:
Thomas stood 12.0 m from the base of a tree.
=> Horizontal distance = 12 m
Let say height of tree = H m
Thomas held the clinometer 2.2 m about the ground.
=> Height above clinometer = H - 2.2 m
The angle shown on the clinometer was 70°.
=> angle of elevation = 70°
tan 70° = (h - 2.2)/12
=> 2.747 = (h - 2.2)/12
=> 32.96 = h - 2.2
=> h = 32.96 + 2.2
=> h = 35.16
=> h = 35.2
height of the tree to the nearest tenth of a metre. = 35.2 m
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