A passanger of an aeroplane observes that Howrah station is at one side of the plne and Saheed Minar is just on the opposite side. The angles fo depression of Howrah station and Saheed Minar from the passanger of aeroplane are `60^(@) and 30^(@)` respectively. If the aeroplane is at a height of `545sqrt(3)` metres at that time, find the distance between Howrah station and Saheed Minar.

Explanation

Let the position of Howrah station be H and the position of Saheed Minar be S. OD is the height of the aeroplane.
As per question OD =`545sqrt(3)` metres,
`angleEOH = angleOHD = 60^(@) and angleFOS = angleOSD = 30^(@)`
Now, from the right-angled triangle OHD, we get,
`tan 60^(@) =(OD)/(HD)` [by definition]
`sqrt(3) = (545sqrt(3)/(HD))`
or, HD =545
Also, from the right-angled triangle OSD, we get,
`tan 30^(@) =(OD)/(HD)` [by definition]
or, ` (1)/(sqrt(3))=(545sqrt(3))/(DS)`
or, DS = `545sqrt(3) xxsqrt(3)`
or, DS = `545 xx 3`
=1635
Now, HS = HD + DS
= 545 + 1635
=2180
Hence the distance between station and Saheed Minar is 2180 metres.