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A tower stands vertically on level ground and its top is observed from different points on the ground.
Which one of the following statements is TRUE?

Class 10Heights and DistancesTrigonometry
  • AIf the angle of elevation of the top from a point on the ground is 45°, the height of the tower equals the distance of that point from the foot of the tower.
  • BThe angle of elevation of the top is the same from every point on the ground.
  • CThe height of the tower can be found from the angle of elevation alone, without knowing any distance.
  • DAs a point moves closer to the foot of the tower, the angle of elevation of the top becomes smaller.

Step-by-Step Solution

tan 45 = 1, so and the height equals the distance. The angle changes from point to point and grows LARGER as the point comes closer, so one angle alone is never enough without a measured length.
Answer: A) If the angle of elevation of the top from a point on the ground is 45°, the height of the tower equals the distance of that point from the foot of the tower.

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