The angle of elevation to the top of a Building in New York is found to be 5 degrees from the ground at a distance of 2 miles from the base of the building. Using this information, find the height of the building.

We are given:

Horizontal distance of the point of observation from the building = 2 miles

Angle of elevation of the building = 5 degrees

Finding the height of the Building:

Let the height of the building be x miles

In the given case, the following right-angled triangle will be formed

We know that:  Tan(θ) = Opposite / Adjacent

So, Tan(5°) = x / 2

0.0875 = x/2                                   [since Tan(5°) = 0.0875 ]

x = 0.175                                         [Multiplying both sides by 2]

Height in Meters:

We know that 1 mile = 1609.344 meters

So, we can say that:

1609.344 meters / 1 mile  =  1

Multiplying the height of the building by 1

0.175 miles * 1

since 1 = 1609.344 meters / 1 mile:

0.175*1609.344 meters

Here, the 'miles' in the numerator and the denominator will cancel out

281.6 meters

Hence, the height of the Building is 281.6 m OR 0.175 miles

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