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

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°.