Solution:
The problem asks to find the height of the tree. Since the sides involved in this problem are the opposite and adjacent sides, we will use tan θ. The formula we will use in this problem is
tan θ = h / x
where:
θ = angle of elevation
h = height
x = length of the casted shadow
Listing the given data
θ = 54°
x = 9.2 ft
Solving for h
tan θ = h / x
h = x tan θ
h = (9.2 ft)(tan 54°)
h = 12.66 ft
Therefore, the height of the tree is 12.66 ft.
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