Q. 37 B

# A flagstaff stands on the top of a tower. At a point distant d from the base of the tower, the angles of elevation of the top of the flagstaff and that of the tower are ]3 and a respectively. Prove that the height of the flagstaff is = d (tanβ – tan α).

Answer :

From the ∆DBC,

Now from the ∆ABC,

Put the value of DC from the equation(i)

So,

Therefore, height of the flagstaff is .

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PREVIOUSA 10 m high flagstaff stands on a tower. From a point on the level ground, the angles of elevation of the foot and top of the flagstaff are 30° and 60° respectively. Find the height of the tower.NEXTA vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane, the angle of elevation of the bottom of the flagstaff is α and that of the top of the flagstaff is β. Prove that the height of the h tan a tower is .