Multiple choice

Horizontal distance between two pillars of different height is 60 m. it was observed that the angular elevation form form the top of the shorter pillar to the top of the taller pillar is $\displaystyle 45^{\circ}$ if the height of taller pillar is 130 m, the height of the shorter pillar

  1. 45 m

  2. 70 m

  3. 80 m

  4. 60 m
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B Correct answer
Explanation

The angle of elevation is 45 degrees with horizontal distance 60 m, so the height difference equals 60 * tan(45 deg) = 60 m. The shorter pillar height is 130 - 60 = 70 m.

AI explanation

Let the height of the shorter pillar be h meters. Since the angle of elevation from the shorter pillar to the taller one is 45 degrees, the tangent ratio yields tan(45 degrees) equals the difference in heights divided by the horizontal distance. This gives 1 equals (130 minus h) divided by 60. Solving this equation results in 60 equals 130 minus h, so h equals 70 meters.

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