Multiple choice

The upper three-quarters of a vertical pole subtend an angle tan-1(3/5) at a point in the horizontal plane through its foot at a distance of 40 m from it. What is the height of the pole?

  1. 80 m

  2. 100 m

  3. 160 m

  4. 200 m
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C Correct answer
AI explanation

Let the total height of the pole be H, meaning the upper three-quarters starts at a height of one-quarter of H. Using the angle of elevation formula, the tangent of the angle to the top minus the tangent of the angle to the lower point equals the difference in height divided by the distance. This translates to tan inverse of 3 divided by 5 minus tan inverse of H divided by 160. Simplifying the tangent of the difference of two angles gives the equation 3 divided by 5 equals the quantity 160 minus H divided by 160, which is all divided by the quantity 1 plus H divided by 160. Solving the equation 960 equals 25600 minus 160H yields H equals 160 meters.

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