Question

19. Two poles of equal heights are standing opposite to each other on either side of the
river, which is 80 m wide. From a point between them on the road, the angle of
elevation of the top of the poles are 60° and 30° respectively. Find the height of the
poles and the distances of the point from the poles.​

Answer 1

Answer:

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here is ur answer

Answer 2

Answer:

20√3, 20 m and 60 m.

Step-by-step explanation:

Let AB and DE be the two poles, and C be the point of observation.

Width of road, BD =  80 m.

Angle of elevation to AB, ∠ACB = 30°.

Angle of elevation to DE, ∠ ECD = 60°.

In ΔACB,

tan30° = AB/BC

=> 1/√3 = AB/BC

=> AB = BC/√3        -------- (1)

In Δ EDC:

tan60° = ED/CD

=> √3 = ED/80 - BC

=> ED = √3(80 - BC)    ------ (2)

It is said Two poles of equal heights .

AB = ED.

Hence, from (1) and (2),

BC/√3 = √3(80 - BC)

=> BC = √3(80 - BC)

=> BC = 60 m.

Place value in (1),

AB = 20√3 m

Then,

tan60° = ED/CD

=> √3 = 20√3/CD

=> CD = 20 m.

Therefore,

Height of Pole = 20√3 m.

Distances of point = 20 m and 60 m.

#Hope my answer helped you!