Height and distance problems use right-angled triangles. The line of sight, the horizontal ground and the vertical object form a triangle, and trigonometric ratios link the sides.
1Angles
Angle of elevation: measured upwards from the horizontal to the line of sight
Angle of depression: measured downwards from the horizontal; it equals the angle of elevation from the other point
2Ratios
tan θ = perpendicular/base, sin θ = perpendicular/hypotenuse, cos θ = base/hypotenuse
tan 30° = 1/√3, tan 45° = 1, tan 60° = √3
sin 30° = cos 60° = 1/2, sin 60° = cos 30° = √3/2, sin 45° = cos 45° = 1/√2