Question

Two hoardings on cleanliness are put on two poles of equal heights standing opposite to each other on either side of the road, which is 80m wide. From a point between them on the road l, the angles of elevation are 60°and 30° respectively. Find the height of the poles and the distance of the point from the poles.

Answer 1

ur required answer is here

Answer 2

Answer:

Distance from right pole to the point C = x = 20 m

Distance from left pole to the point C = 80 - x = 80 - 20 = 60 m

Height of the pole, $h=20 \sqrt{3} m$

Step-by-step explanation:

From the drawn figure, we get

AB = DE = pole = h

BE = road = 80 m

Let C be a point on road BE, such that, BC = (80 - x) and CE = x

To find :

• height of the poles and the distances of the point from the poles.
• tangent of the angle in both the triangles

Step 1

$&\tan 30^{\circ}=\frac{A B}{B C}=\frac{h}{80-x}$

$&\frac{1}{\sqrt{3}}=\frac{h}{80-x} \ldots(i)$

$&\tan 60^{\circ}=\frac{D E}{C E}=\frac{h}{x}$

$&\sqrt{3}=\frac{h}{x} \ldots(ii)$

Step 2

Divide (ii) from (i)

$&\frac{\sqrt{3}}{\frac{1}{\sqrt{3}}}=\frac{\frac{h}{x}}{\frac{h}{80-x}}$

$&3=\frac{80-x}{x}$

4x = 80

x = 20 m

Distance from right pole to the point C = x = 20 m

Distance from left pole to the point C = 80 - x = 80 - 20 = 60 m

Step 3

Substitute the value of x in (ii)

$&\sqrt{3}=\frac{h}{x}$

$&h=20 \sqrt{3} m$

Height of the pole, $h=20 \sqrt{3} m$

Therefore,

Distance from right pole to the point C = x = 20 m.

Distance from left pole to the point C =80 - x = 80 - 20 = 60 m.

Height of the pole, $h=20 \sqrt{3} m$.

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