From a point 20 m from the base of a vertical tower, the angle of elevation of the top is 45°. Find the height of the tower (in metres).

Introduction / Context:
A 45° elevation to a vertical object on level ground gives a one-to-one relation between height and horizontal distance.

Given Data / Assumptions:

• Horizontal distance x = 20 m; θ = 45°.

Concept / Approach:
tan 45° = height/x = 1 ⇒ height = x.

Step-by-Step Solution:

Verification / Alternative check:
If the angle were 30°, height would drop to 20/√3 ≈ 11.55 m; if 60°, it would increase to 20√3 ≈ 34.64 m.

Why Other Options Are Wrong:
10 m halves the correct value; 40 m doubles it; 20√3 m corresponds to 60°, not 45°.

Common Pitfalls:
Using sine or cosine; misreading 20 m as vertical instead of horizontal.

Final Answer:
20 m