Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles 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.

Asked by Abhisek | 1 year ago |  84

##### Solution :-

As per above figure, AB = CD,

OB + OD = 80 m

Now,

In right ΔCDO,

tan 30° = $$\dfrac{CD}{OD}$$

$$\dfrac{1}{\sqrt{3}}$$ = $$\dfrac{CD}{OD}$$

CD =  $$\dfrac{OD}{\sqrt{3}}$$… (1)

Again,

In right ΔABO,

tan 60° = $$\dfrac{AB}{OB}$$

$$\sqrt{3}$$ = $$\dfrac{AB}{80-OD}$$

AB = $$\sqrt{3}(80-OD)$$

AB = CD (Given)

$$\sqrt{3}(80-OD)$$$$\dfrac{OD}{\sqrt{3}}$$ (Using equation (1))

3(80-OD) = OD

240 – 3 OD = OD

4 OD = 240

OD = 60

Putting the value of OD in equation (1)

CD = $$\dfrac{OD}{\sqrt{3}}$$

CD = $$\dfrac{60}{\sqrt{3}}$$

CD = $$\dfrac{20}{\sqrt{3}}$$ m

Also,

OB + OD = 80 m

⇒ OB = (80-60) m = 20 m

Thus, the height of the poles are $$20\sqrt{3}$$ m and distance from the point of elevation

are 20 m and 60 m respectively.

Answered by Pragya Singh | 1 year ago

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