One tower has a height of 300 metres. From the top of another tower standing on the same level ground and 120 metres away horizontally, the angle of depression of the top of the 300 m tower is 60°. What is the height of this smaller tower (in metres)?

Introduction / Context:
This height-and-distance question involves two towers of different heights. From the top of one tower, the top of the other is seen below the horizontal line of sight, giving an angle of depression. By relating the vertical difference in heights to the horizontal separation, we can use the tangent function to find the unknown height.

Given Data / Assumptions:

• Tower A has a known height of 300 m.
• Tower B has unknown height h and is referred to as the smaller tower.
• Horizontal distance between the bases of the two towers = 120 m.
• From the top of Tower A, the angle of depression of the top of Tower B is 60°.
• The ground between the towers is level.

Concept / Approach:
An angle of depression from the horizontal line at the top of Tower A down to the top of Tower B corresponds to an angle of elevation of 60° from Tower B up to that horizontal line. The vertical difference in height between the two towers is (300 − h). Using the right triangle formed by this vertical difference and the horizontal distance, we apply:
tan(60°) = (vertical difference) / (horizontal distance)and solve for h.

Step-by-Step Solution:
Let h be the height of the smaller tower (Tower B).Vertical difference between tops = 300 − h.Horizontal distance between towers = 120 m.Given angle of depression = 60°, so:tan(60°) = (300 − h) / 120.We know tan(60°) = √3.Thus: √3 = (300 − h) / 120.So, 300 − h = 120√3.Therefore, h = 300 − 120√3.Using √3 ≈ 1.732: 120√3 ≈ 120 * 1.732 = 207.84.Hence, h ≈ 300 − 207.84 = 92.16 m, which matches the option 92.15 m when rounded.

Verification / Alternative check:
We can quickly verify: vertical difference ≈ 207.84 m and horizontal distance 120 m, so tan(60°) ≈ 207.84 / 120 ≈ 1.732, which equals √3. This agrees with the given angle of depression and confirms the correctness of the height found.

Why Other Options Are Wrong:
88.24 m, 106.71 m, 112.64 m, 120 m: These heights lead to vertical differences that do not satisfy (300 − h) / 120 = √3. Substituting any of them will produce tangent values different from tan(60°).

Common Pitfalls:
Some students mistakenly compute h = 300 + 120√3, making the smaller tower taller than the 300 m one. Others confuse angle of elevation and depression or forget that the angle is formed with the horizontal, not with the vertical. Always draw a diagram and mark the vertical difference and horizontal distance clearly to avoid sign and interpretation errors.

Final Answer:
The height of the smaller tower is approximately 92.15 m.