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
[tex]0.175 miles * \frac{1609.344 meters}{1 mile}[/tex]
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
