A flag staff stands on the top of a 5m high tower. From a point on the ground, the angle of elevation of the top of the flagstaff is 60 0 and from the same point, the angle of elevation of the top of the tower is 45 0 . Find the height of the flag staff.
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Since the height of the tower is 5m, and the top of the tower from a point on the ground makes an angle of 45 degrees, the distance of the point from the base of the tower is 5m.
Since the top of the flag post is making an angle of 60 degrees from the point, the top of the flag post is at a height of 5+x from the base of the tower, where x is the height of the flag post.
Thus, we get a right angle triangle with a base of 5m, and height of 5+x m, and the top of the flag post making an angle of 60 degrees with the horizontal.
We know that tan 60 = sqrt 3 = opposite / adjacent = (5+x) / 5
Therefore, 5*sqrt 3 = x+5
Or x = 5*sqrt 3 - 5 = 5 * (sqrt 3 - 1) = 5 * (1.732 - 1) = 5 * 0.732 = 3.66m.
Thus, the height of the flag post is 3.66m.
Since the top of the flag post is making an angle of 60 degrees from the point, the top of the flag post is at a height of 5+x from the base of the tower, where x is the height of the flag post.
Thus, we get a right angle triangle with a base of 5m, and height of 5+x m, and the top of the flag post making an angle of 60 degrees with the horizontal.
We know that tan 60 = sqrt 3 = opposite / adjacent = (5+x) / 5
Therefore, 5*sqrt 3 = x+5
Or x = 5*sqrt 3 - 5 = 5 * (sqrt 3 - 1) = 5 * (1.732 - 1) = 5 * 0.732 = 3.66m.
Thus, the height of the flag post is 3.66m.
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