Height of building?What should the height of a building be so that a ladder which is 80 m long and is placed 60 m away from the building forms an...

From the information in the question we know that the
ladder is placed 60 meters away from the building, it is 80m long and the angle that is
has to form with the building should be less than 60
degrees.

Now, we assume that the building is a vertical
structure.

Therefore a right angled triangle is formed with
between the ground, the building and the ladder, with the ladder acting as the
hypotenuse. As the angle formed by the ladder and the ground should be less than 60
degrees, let’s take the extreme case of 60 degrees. When this is the case we see that
sin 30 = height of the building/ length of the ladder =   sqrt 3
/2

=> height of the building = (sqrt
3/2)*80

=> height of the building = 69.28
m

The angle for any height more than 69.28 m exceeds 60
degree.

Therefore the required height of the
building cannot exceed 69.28 m.