Two poles are 200 m apart if from the middle point of the line joining their feet an observer finds the angle of elevation of their tops as 60 and 30 degree respectively then find the ratio of the height of the poles
Answers
The ratio of the height of the poles is 3:1.
Step-by-step explanation:
Referring to the figure attached below, let's make some assumptions
AB = h₁= height of the first pole
ED = h₂ = height of the second pole
BD = distance between the two poles = 200 m
Point C = midpoint of BD ∴ BC = CD = 1/2 * 200 = 100 m
Angle of elevation from point C to the top of AB = θ₁ = 60°
Angle of elevation from point C to the top of ED = θ₂ = 30°
Now,
Consider ΔABC, applying the trigonometric ratios of a triangle, we get
tan θ₁ = perpendicular/base
⇒ tan 60° = AB/BC
⇒ tan 60° = h₁/100
⇒ √3 = h₁/100
⇒ h₁ = 100√3 m ...... (i)
and,
Consider ΔEDC, applying the trigonometric ratios of a triangle, we get
tan θ₂ = perpendicular/base
⇒ tan 30° = ED/CD
⇒ tan 30° = h₂/100
⇒ 1/√3 = h₂/100
⇒ h₂ = 100/√3 m ...... (ii)
Thus, from (i) & (ii), we get
The ratio of the height of the two poles is given by,
= h₁/h₂
= [100√3] / [100/√3]
= √3 × √3
= 3:1
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