SSC MTS Heights & Distances

When you look up at a tall building, the angle your line of sight makes with the horizontal ground is called the angle of elevation. When you look down from a height, it's called the angle of depression. These angles help us calculate heights and distances we cannot measure directly

The angle of elevation from point A to point B equals the angle of depression from point B to point A. Always draw a right triangle and identify the opposite side, adjacent side, and hypotenuse clearly. The horizontal distance remains constant in most problems

• tan θ = Height/Base (most used) • sin θ = Height/Hypotenuse • cos θ = Base/Hypotenuse • When angle changes from α to β: New height = Base × (tan β - tan α) + Original height

tower/building height from given distance, finding distance when height is known, problems involving two angles of elevation, lighthouse/ship problems, and ladder-wall problems

When moving closer or farther from an object, use the formula: h = d₁ × tan α = d₂ × tan β, where h is height, d is distance, and α, β are angles. This eliminates the need to calculate height separately

For 30-60-90 triangles, use ratio 1:√3:2. For 45-45-90 triangles, use ratio 1:1:√2. When angle of elevation doubles, use the identity tan(2θ) = 2tan(θ)/(1-tan²θ). Remember that complementary angles have reciprocal trigonometric ratios.