Question

Two poles are ‘2x’ meters apart. If from the middle point of the line joining their feet an

observer finds the angle of elevations of their tops as 600 and 300

respectively, then

the ratio of the height of the poles is?​

Answer 1

Given :- (from image)

• AB and ED are poles .
• ∠ACB = 60°
• ∠EDC = 30°
• BD = 2x meters .
• C is mid Point of BD .

To Find :-

• AB : ED = ?

Solution :-

In right ∆ABC, we have,

→ Tan 60° = AB / BC

→ √3 = AB / x

→ AB = √3x m.

In right ∆EDC, we have,

→ Tan 30° = ED / CD

→ 1/√3 = ED / x

→ √3ED = x

→ ED = (x/√3)

→ ED = (x/√3) * (√3/√3)

→ ED = (√3x/3) m.

therefore,

→ AB : ED = √3x : (√3x/3)

→ AB : ED = 1 : (1/3)

→ AB : ED = 3 : 1 (Ans.)

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