Question

Question 4.

The angle of elevation of the top of a tree from a point on the ground 22 m away is 24⁰°.
Calculate the height of the tree (in metres) correct to 2 decimal places.
22 m
tree

Answer 1

9.80 m

Explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between sides of a right triangle and its angles.

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setup

The geometry of this problem can be modeled by a right triangle, so these relations apply. We are given an angle and adjacent side, and asked for the opposite side, so the relation of interest is ...

Tan = Opposite/Adjacent

Using the given values, we have ...

tan(24°) = AC/AB = (tree height)/(distance from tree)

tan(24°) = AC/(22 m)

solution

Multiplying by 22 m gives ...

tree height = AC = (22 m)·tan(24°) ≈ 9.79503 m

The height of the tree is about 9.80 meters.