Question

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Q1. A ladder 9 m long reaches to a point below the top of building. From the foot of the ladder, the angle of olevation of the building is 60°. Find the height of the building. Here the ladder makes the angle 45° with ground. (Ans=11.02m)

Q2. A vertical pole is divided in the ratio 9:1 .If both segments of pole subtend equal angles to each other at a distance of 20m away from the foot of pole, find height of pole. (Ans=178.8m)



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Answer 1

Q 1 : Solution:

Let the height of the building be h.

We know that tan(60) = h/9 (angle of elevation formula)

h = 9tan(60) = 9sqrt(3)/3 = 3*sqrt(3) = 3.464101615 m (approx)

Q 2 : Solution:

Let the height of the pole be h.

Let the shorter segment be x, and the longer segment be 9x.

We know that tan(theta) = x/(20) = 9x/(20+h) (angle subtended formula)

By cross multiplying and simplifying, we get:

x = (20h)/(h+180)

The ratio of the segments is x:9x = 1:9, so x = (20h)/(h+180) = 1/10 * h

h = 10x = (20h)/(h+180)

h^2 + 180h - 20h^2 = 0

h(20-h) = 0

h = 0 or h = 20

Since the pole has a height, h = 20m is not possible, so the height of the pole is h = 178.8m