Q1
The angle of depression is formed when looking:
Adown at an object
Bup at an object
Csideways at an object
Ddirectly at the horizon
CBSEClass 10 (CBSE)MathematicsCh 9 · Topic 2
Heights and Distances - Angle of Depression
Learning to solve problems involving the angle of depression.
Core concept
A key geometric relationship exists: the angle of depression from a higher point to a lower point is always equal to the angle of elevation from that lower point back up to the higher point, since these are alternate angles formed by the horizontal lines (which are parallel) and the shared line of sight. For example, from the top of a 50m cliff, if the angle of depression to a boat is 30°, using tan(30°) = 50/distance, the boat's distance from the cliff's base can be calculated as distance = 50/tan(30°) ≈ 86.6m.
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Quick notes
• The angle of depression is the downward angle from horizontal to a line of sight towards an object below.
• The angle of depression equals the angle of elevation viewed from the opposite point (alternate angles).
• Example: from a 50m cliff with 30° angle of depression, distance to boat ≈ 86.6m.
• These angles are equal because the two horizontal lines involved are parallel.