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The top of a 20 m high building makes an angle of elevation of 60 with the bottom of an electric pole and angle of elevation of 30 with the top of the pole. What is the height of the electric pole?

The top of a 20 m high building makes an angle of elevation of 60 with the bottom of an electric pole and angle of elevation of 30 with the top of the pole. What is the height of the electric pole? Correct Answer 40 / 3 m

Let the height of the pole be h m and base distance be b m. ➩ tan 60 = height / base distance ➩ √3 = 20 / b ➩ b = 20 / √3 m Also, ➩ tan 30 = height / base ➩ 1 / √3 = 20 – h / b ➩ b = (20 – h) √3 On equating the two equations: ➩ 20 / √3 = (20 – h) √3 ➩ 20 = 3(20 – h) ➩ 20 = 60 – 3h ➩ 3h = 40 ➩ h = 40 / 3 m

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