Question

The base of a cliff is circular. From the extremities
of a diameter of the base the angle of elevation of
the top of the cliff are 30° and 60°. If the height of
the cliff be 500 metres, then the diameter of the
base of the cliff is :​

Answer 1

Answer:

Let the distance from the foot of the cliff to one extreme be x and other extreme be y. Then

tan30 =500/x and tan60 =500/y

1/√3 = 500/x and √3 = 500/y

x=500√3 and y= 500/√3

diameter = x + y= 500√3 + 500/√3

=500(√3 + 1/√3)=500(3+1)/√3=500×4×√3/3=

1154.67 Ans