Rocio is 5.5 feet tall.
What is angle of elevation?
The angle of elevation is an angle that is formed between the horizontal line line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is called angle of elevation.
According to the question
The height of the pole, AB = 27.5 ft
Length of the shadow, BC = 45 feet
Distance of Rocio from the base of the pole, BD = 36 feet
Let angle of elevation be θ and height of Rocio be x feet.
Now, in triangle ABC we have,
[tex]tan[/tex]θ = [tex]\frac{AB}{BC}[/tex]
⇒ tanθ = [tex]\frac{27.5}{45}...(i)[/tex] (tanθ = perpendicular/ base)
Similarly, in triangle CED we have
tanθ = [tex]\frac{x}{CD}[/tex]
⇒ tanθ = [tex]\frac{x}{BC-BD}[/tex]
⇒ tanθ = [tex]\frac{x}{45-36}[/tex]
⇒ tanθ = [tex]\frac{x}{9}..(ii)[/tex]
From equation i and ii
[tex]\frac{x}{9} =\frac{27.5}{45}[/tex]
⇒ [tex]x = \frac{27.5}{5} =5.5 feet[/tex]
Hence, Rocio is 5.5 feet tall.
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