Height and Distance

Height and Distance

Angles of Elevation  and Depression : Suppose we are viewing an object. The line of sight or the line of vision is a straight line from our eye to the object we are viewing.

* if the object is above the horizontal from the eye, we have to lift up our head to view the object. In this process, our eyes move through an angle. This angle is called the angle of elevation of the object.

* if the object is below the horizontal from the eye, then we have to turn our head downwards to view the object, in this process, our eyes move through an angle this angle is called the angle of depression of the object.

Problem : 1 A  small boy is standing at some distance a flags pot. When he sees the flag, the angle of elevation formed is  If the height of the flag post is 30m, what is the distance of the child from the flag post?

Problem 2: 300 m from the foot of a chiff on level ground, the angle of elevation of the top of a chiff is 30°. Find the height of this chiff.

Sol: Let the height of the chiff AB be x m.

Problem 3 : A man wishes to find the height of a flagpost which stands on horizontal plane; at a point on this plane, he finds the angle of elevation of the top of the flag post to be 45°. On walking 30m towards the tower, he finds the corresponding angle of elevation to be 60°. Find the height of the flag post.

Problem 4 : the angles of elevation of the top and bottom of a flag kept on a flag post from 30m distance are 45° and 30° respectively. What is the height of the flag?

Problem : 5  The horizontal distance between two towers is . the angle of depression of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 160m, find the height of the first tower.

Sol :

Problem :6 Two poles of equal heights stand on either side of a roadway which is 120m wide. At a point on the roadway between the poles, the elevations of the tops of the pole are 60° and 30° respectively. Find the heights of the poles and the position of the point.

Sol:

Problem 7: The length of a string between a kite and a point on the ground is 102m. if the string makes an angle  with the level ground such that  how high is the kite?

Problem 8 : The angles of depression of two ships from the top of a lighthouse are 45° and 30°. If the ships are 100m apart, find the height of the light house.

Problem 9 : From the top of cliff, 200m high, the angles of depression of two boats which are due south of observer are 60° and 30°. Find the distance between the two boats.

Problem 10: From the top and bottom of a building of height h, the angles of elevations of the top of a tower are  and  respectively. Find the height of the tower.

Problem 11: A vertical tower stands on a horizontal plane and is surmounted by a Vertical flag staff of height h. At a point on the plane, the angles of elevations of the bottom of the flags staff is  that of the top of the flag staff is . Find the height of the tower.

Sol: