Question

Asked Sep 23, 2019

On level ground, you stand 27.0 m from the base of a tree and determine that the treetop is at 42 degrees above the horizontal, as measured from ground level. How do you figure out how tall the tree is conceptually?

Step 1

Consider the following diagram, which represents the situation mentioned in the question. Here, *AB* is the tree’s height and *AC* is the distance of base of the tree from the observing person such that the angle *ACB* is equal to 42 degrees. Note that the triangle *BAC* forms a right triangle.

Step 2

Use the trigonometric expression for the tangent of an angle to write the tangent of the angle *ACB* as,

Step 3

Here, *AB* is the perpendicular length and *AC* is the base length for the a...

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