A man 3 m above the surface of a lake observes a cloud and its reflection in the lake. The angle of elevation of the cloud equals the angle of depression of its reflection.
True.
Step 1: The man is standing at a point 3 m above the surface of the lake (height measured in SI units).
Step 2: The cloud is above the lake. Its reflection will appear the same distance below the surface of the lake, because water acts like a horizontal mirror.
Step 3: From the man’s eye, one line of sight goes upward to the real cloud (this is the angle of elevation), and another line of sight goes downward to the reflection (this is the angle of depression).
Step 4: The vertical distance from the man’s eye to the cloud is the same as the vertical distance from his eye to the reflection. This is because the reflection is located symmetrically below the water surface.
Step 5: These equal vertical distances form two identical right-angled triangles — one with the cloud and one with the reflection.
Step 6: Since the two triangles are congruent, the angle of elevation (to the cloud) is equal to the angle of depression (to its reflection).
Therefore, the statement is True.