Question

A tower stands vertically on the ground from a point on the ground which is 25 m away from the foot of the tower. If the height of the tower is 25√5 meters, find the angle of elevation.

Option 1) 30° Option 2) 90° Option 3) 60° Option 4) 120°

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Answer

To determine the angle of elevation, we can use trigonometric principles:

  1. We have a right triangle where:

    • The adjacent side (distance from the point on the ground to the foot of the tower) is 25 meters.

    • The opposite side (height of the tower) is $ 25\sqrt{5} $ meters.

  2. Let $ \theta $ be the angle of elevation.

  3. We apply the tangent function of the angle $ \theta $: $$ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{25\sqrt{5}}{25} = \sqrt{5} $$

  4. We need to find $ \theta $ such that: $$ \tan(\theta) = \sqrt{5} $$

$$ \tan(\theta) = \sqrt{5} $$

is more accurately represented at:

$$ \tan \left (60^\circ \right) $$

Hence, the angle of elevation ( \theta ) is 60°.

Therefore, the correct option is Option 3: 60°.


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