Angles

Let the height of the tower be , and let the initial distance from point to the foot of the tower be . After walking a distance towards the tower, the new distance to the foot of the tower becomes .

Step 1: Use the tangent function for both angles of elevation.

From point , the angle of elevation is , so:

After walking a distance , the angle of elevation becomes , so:

Step 2: Substitute into .

Rearrange to isolate :

Factor out :

Step 3: Simplify using cotangent identities.

Recall that . Substituting this:

Solve for :

Final Answer: The height of the tower is , which corresponds to option .

Step 1: Represent the problem using trigonometry.

Let the height of the tower be , and let the length of the shadow be . From the problem, we know:

The angle of elevation of the Sun is the angle between the ground and the line from the top of the tower to the tip of the shadow. Using the tangent function:

Step 2: Substitute .

Step 3: Determine the angle .

The value of corresponds to .

Final Answer: The angle of elevation of the Sun is , which corresponds to option .