Right triangle at a house corner: At a point 15 m from the base of a 15 m high house on level ground, what is the angle of elevation of the top of the house?

Introduction / Context:Equal opposite and adjacent sides in a right triangle imply a 45° angle of elevation by the tangent definition.

Given Data / Assumptions:Height = 15 m; horizontal distance = 15 m; level ground; vertical wall.

Concept / Approach:tan θ = opposite/adjacent = 15/15 = 1 → θ = 45°.

Step-by-Step Solution:

Verification / Alternative check:Pythagoras gives hypotenuse 15√2; this corresponds to an isosceles right triangle.

Why Other Options Are Wrong:30° or 60° would require unequal legs; 90° is impossible for a finite distance.

Common Pitfalls:Using sine instead of tangent; confusing angle at the top vs at the observer.

Final Answer:45°