Question

If the angles of elevation of the top of a tower from three collinear points a, b and c on a line leading to the foot of the tower, are 30,45 and 60 respectively, then the ratio ab : bc, is:

Answer 1

This may help you......

Answer 2

The ratio ab:bc is √3:1

Let the tower have height h and it starts from point o.

For angle 60° :-

Tan 60° = h/oc

√3 = h/oc

Oc = h/√3

For angle 45°:-

Tan45° = h/ob

Ob=h

For angle 30°:-

Tan 30° = h/oa

1/√3=h/oa

oa = √3h

ab = oa- ob

bc = ob-oc

ab:bc = (√3h - h):(h - h/√3)

ab:bc= (√3-1):(1-1/√3)

ab:bc= √3:1