Question

Two poles of equal height are standing opposite each other on either side of the road 80m wide. From a point between them on the road the angles of elevation of the top of the two poles are respectively 60° and 30°.Find the distance of the point from the two poles.​

Answer 1

Step-by-step explanation:

let AB and CD are the two poles of equal height

which are 80m apart

in ∆AOB

tan 60° = AB/ OB =√3 = AB/OB = AB = OB√ 3

since the height of the poles is equal

CD = AB = OB √3 ....... (1)

now in ∆ COD

tan 30° =. CD/OD = 1/√3 = OB √3 /80 -OB

= 80 - OB = 30B = OB = 20

and OD = 80 - 20 = 60

from the equation (1) AB = CD = 20√3

hence the required height of the poles is 20√3 m

and the distance of the point from the poles

are 20m and 60m

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