Question

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From point between them on the road, the angles of elevation of the top of poles are 60° and 30°, respectively. Find the height of the poles and the distance of the point from the poles.
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Answer 1

here is a answer

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Answer 2

$\huge\star{\pink{\underline{\underline{\tt{Explanation:}}}}}$

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• Let AB and CD be the poles of equal height.

• O is the point between them from where the height of elevation taken. BD is the distance between the poles

As per above figure, AB = CD,

$\mapsto$OB + OD = 80 m

Now,

In right ΔCDO,

$\leadsto$tan 30° = CD/OD

$\leadsto$1/√3 = CD/OD

$\leadsto$CD = OD/√3 … (1)

Again,

In right ΔABO,

$\leadsto$tan 60° = AB/OB

$\leadsto$√3 = AB/(80-OD)

$\leadsto$AB = √3(80-OD)

$\leadsto$AB = CD (Given)

$\leadsto$√3(80-OD) = OD/√3 (Using equation (1))

$\leadsto$3(80-OD) = OD

$\leadsto$240 – 3 OD = OD

$\leadsto$4 OD = 240

$\leadsto$OD = 60

Putting the value of OD in equation (1)

$\leadsto$CD = OD/√3

$\leadsto$CD = 60/√3

$\leadsto$CD = 20√3 m

Also,

$\leadsto$OB + OD = 80 m

⇒ OB = (80-60) m = 20 m

Thus, the height of the poles are 20√3 m and distance from the point of elevation are 20 m and 60 m respectively.