A man observes the angles of elevation of the top of a building to be 30sup0sup He walks towards it ...

Question

A man observes the angles of elevation of the top of a building to be 30sup0sup He walks towards it in a horizontal line through its base On covering 60 m the angle of elevation changes to 60sup0sup Find the height of the building correct to the nearest decimal place

Accepted Answer

Solution A commonly used concept in relation to height and distance is the angle of elevation particularly in trigonometry It is described as a relationship between an oblique line from the observers eye to an item above his eye and the horizontal plane It is given that AB is a building whose height be x CD 60 m In ABC tan 60sup0sup xBC 3 xy So we get y x3 1 In ABD tan 30sup0sup ABBD 13 x y 60 By cross multiplication y 60 3 x y 3 x 60 Using both the equations we get x3 3 x 60 By further calculation x 3x 603 3x x 60 1732 So we get x 60 1732 2 x height of building AB 5196 m

ML Aggarwal Solutions Class 10 Mathematics Solutions for Heights and Distances Exercise 20 in Chapter 20 - Heights and Distances