Answer
Find out the what is the height of the pole .
To proof
As given
A person is standing exactly 36 ft from a telephone pole.
There is a 30° angle of elevation from the ground to the top of the pole.
By using the trignometric identity
[tex]tan\theta = \frac{Perpendicular}{Base}[/tex]
Here Base = 36 ft
[tex]\theta = 30^{\circ}[/tex]
put the value in trignometric identity
[tex]tan30^{\circ} = \frac{Height}{36}[/tex]
[tex]tan30^{\circ} = \frac{1}{\sqrt{3}}[/tex]
Put in the above
[tex]Height = \frac{36}{\sqrt{3}}[/tex]
[tex]\sqrt{3} = 1.732[/tex]
[tex]Height = \frac{36}{1.732}[/tex]
The height of the pole is 20 .79 ft (approx) .
Hence proved
To solve the problem we will use the tangent of the trigonometric functions.
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
The height of the pole is 20.784 ft.
Given to us
To solve the problem assume an imaginary right-angled triangle that is been formed as shown below,
In ΔABC,
[tex]\rm{Tan(\theta) = \dfrac{Perpendicular}{Base}[/tex]
[tex]Tan(\angle C) = \dfrac{AB}{BC}[/tex]
Substituting the values,
[tex]Tan(30^o) = \dfrac{AB}{36}\\\\AB = 36 \times Tan(30^o)\\\\AB = 36 \times \dfrac{1}{\sqrt3}\\\\AB = 20.784\ ft[/tex]
Hence, the height of the pole is 20.784 ft.
Learn more about Tangent (Tanθ):
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