A pole 5m high is fixed on the top of a tower.the angle of elevation of the top of the pole observed from a point A on the ground is 60 degree and the angle of depression of the point A from the top of the tower is 45 degree.Find the height of the tower.
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Let the triangle be PQR such that PR is the hypotenuse
A is the point on the tower join it to R
height of pole is 5m => AP=5m
let the height of tower i.e., AQ = x
Angle of elevation from ground to top of the poleis 60 degrees =>
Angle of Depression from the tower to the ground is 45 =>
tan 45 = x/AQ
1 = x/AQ
=> AQ= x
Tan PRQ = PQ/ RQ
Tan 60 = 5 + x/x
root 3 = 5 + x/ x
(root3 )x = 5 +x
(root 3 )x - x =5
x(root 3 - 1 ) =5
x = 5/ (root 3 - 1)
A is the point on the tower join it to R
height of pole is 5m => AP=5m
let the height of tower i.e., AQ = x
Angle of elevation from ground to top of the poleis 60 degrees =>
Angle of Depression from the tower to the ground is 45 =>
tan 45 = x/AQ
1 = x/AQ
=> AQ= x
Tan PRQ = PQ/ RQ
Tan 60 = 5 + x/x
root 3 = 5 + x/ x
(root3 )x = 5 +x
(root 3 )x - x =5
x(root 3 - 1 ) =5
x = 5/ (root 3 - 1)
tokaians:
not clear without figure
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