Standing on a river bank, a person observes the top of a tower on the opposite bank at 45° elevation. Which statement is correct about the river’s breadth compared to the tower’s height?

Introduction / Context:
The 45° angle of elevation to the top of a vertical object on level ground is a signature configuration: the opposite and adjacent legs of the right triangle are equal.

Given Data / Assumptions:

• Angle of elevation θ = 45°.
• Ground is level; tower is vertical.

Concept / Approach:
tan 45° = 1 ⇒ opposite/adjacent = 1 ⇒ height = horizontal distance. Here, the horizontal distance equals the river’s breadth.

Step-by-Step Solution:

Verification / Alternative check:
Any angle greater than 45° would imply H > B; any angle less than 45° implies H < B. With 45°, equality holds.

Why Other Options Are Wrong:
“Half” or “twice” contradicts tan 45° = 1; “None of these” is false because equality is exactly true.

Common Pitfalls:
Confusing sine/cosine with tangent; overlooking that the breadth equals the adjacent side in the triangle.

Final Answer:
Breadth of the river and the height of the tower are equal