Class X : HOTS Question Answers: Math Unit - 6 ii ( Heights & Distance)

Heights & Distance

If the angle of elevation of cloud from a point ‘h’ meters above a lake is QUOTE and the angle of depression of its reflection in the lake is QUOTE , prove that the height of the cloud is QUOTE .

From an aero plane vertically above a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aero plane are observed to be α and β. Show that the height of the aero plane above the road is QUOTE .

Two stations due south of a tower, which leans towards north are at distances ‘a’ and ‘b’ from its foot. If α and β be the elevations of the top of the tower from the situation, prove that its inclination ‘θ’ to the horizontal given by QUOTE

The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is α. On advancing ‘p’ meters towards the foot of the tower, the angle of elevation becomes β. show that the height ‘h’ of the tower is given by h= QUOTE

A boy standing on a horizontal plane finds a bird flying at a distance of 100m from him at an elevation of 300. A girl standing on the roof of 20 meter high building finds the angle of elevation of the same bird to be 450. Both the boy and the girl are on opposite sides of the bird. Find the distance of the bird from the girl

From a window x meters high above the ground in a street, the angles of elevation and depression of the top and the foot of the other house on the