Question

a man observes two vertical poles which are fixed opposite to each other on either side of the road if the width of the road is 90 and height of the pole are in the ratio 1 is to 2 also the angle of elevation of their top from a point between the line joining the foot of the pole on the road is 60 degree the height of the pole find ​

Answer 1

Step-by-step explanation:

The answer for the question is given above

Answer 2

The height of the pole AB = √3 m

height of the pole DE = 60 √3 m

Step-by-step explanation:

here , AB = 1x

DE = 2x

BE = 90 m , let BC = y , CE = 90-y

in triangle ABC

$\tan 60^\circ = \frac{AB}{BC}\\\\tan 60^\circ = \frac{x}{y}\\\\\sqrt{3}y = x..(1)$

in triangle CDE

$\tan 60^\circ = \frac{DE}{CE}\\\\tan 60^\circ = \frac{2x}{90-y}\\\\\sqrt{3}= \frac{2x}{90-y}$

$(90-y)\sqrt{3}= 2x...(2)$

subtracting

$(90-y)\sqrt{3}= 3x \\\\(90-y)\sqrt{3} = 2\sqrt{3} y \\\\90-y = 2y \\\\90=3y \\\\y = 30 m$

$\sqrt{3}y = x\\\\30 \sqrt{3} = x$

now , The height of the pole AB = x = 30 √3 m

height of the pole DE = 2x = 2 (  30 √3) = 60 √3 m

#Learn more :

The angle of elevation of top of a tower from the foot of a 5m tall electric pole is 60 degree and angle of elevation of top of the pole from the top of the tower is 30 degree .find the height of the tower

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