# 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 degrees Option 2) 90 degrees Option 3) 60 degrees Option 4) 120 degrees

## 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:

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.

Let $ \theta $ be the angle of elevation.

We apply the

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