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Question
A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff. At a point on the plane 70 metres away from the tower, an observer notices that the angles of elevation of the top and the bottom of the flagstaff are respectively 60° and 45°. Find the height of the flag-staff and that of the tower.
Solution
Let BC be the tower of height x m and AB be the flagstaff of height y, 70 m away from the tower, makes an angle of elevation are 60° and 45° respectively from top and bottom of the flagstaff.
Let AB = y m, BC = x m and CD = 70 m.
So we use trigonometric ratios.
In a triangle BCD
`=> tan D = (BC)/(CD)`
`=> tan 45^@ = x/70`
`=> 1 = 70/x`
`=> x = 70`
Again in a triangle ADC
`=> tan D = (AB + BC)/(CD)`
`=> tan 60^@ = (y + x)/70`
`=> sqrt3 = (y + 70)/70`
`=> 70sqrt3 = 70 + y`
`=> y = 70(sqrt3 - 1)`
=>y = 51.24
Hence the height of flag staff is 51.24 m and height of tower is 70 m
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