Question

To find the height of a pole a surveyor moves 80 ft away from the base of the pole and then with a transit 4 feet tall measures the angle of elevation to the top of the pole to be 57 degrees. What is the height of the pole?

Answer 1

suppose the part of the pole higher than the transit is x, 
tan57=x/80
x=tan57*80=123
123+4=127
C is the answer.

Answer 2

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The correct option is C, 127 feet.

What is Tangent (Tanθ)?

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,

$\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}$

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.

Let the height of the pole above the eyesight be represented by x.

The given situation can be drawn as shown below. Now, in the triangle made as shown, we can write,

Tan(57°) = Height of the pole above eyesight / Distance between pole and Surveyor

Tan(57°) = x / 80 feet

x = 123.189 feet ≈ 123 feet

Now, the total height of the pole from the ground is,

Height = 123 feet + 4 feet = 127 feet

Hence, the total height of the pole from the ground is 127 feet.

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