Elevation & depression

Measured from the horizontal: An angle of elevation is measured upward from the horizontal to a point above you; an angle of depression is measured downward from the horizontal to a point below you.

Always sketch the horizontal: Draw the horizontal line at the observer's eye first — the angle is between that line and the line of sight.

Not from the vertical: These angles are from the horizontal, never the vertical — a common slip that flips the right ratio.

It's a right-angled triangle: Elevation problems form a right-angled triangle: the height is opposite the angle, the ground distance is adjacent. Use tan (or sin/cos as needed).

Add eye height if given: If the angle is measured from a person's eye (e.g. 1.6 m up), add that to the triangle's height for the true total.

Depression down = elevation up: The angle of depression from a high point down to an object equals the angle of elevation from the object back up — they're alternate angles between two parallel horizontals.

Use the angle inside the triangle: Mark the equal alternate angle at the bottom so the right-angled triangle has the angle in a usable place.

Non-right triangle → sine/cosine rule: When two observation points (or two towers) and an object form a non-right triangle, the sine or cosine rule does the work — exactly as in the audited two-tower elevation question.

Elevation gives one angle: An elevation angle from the same point becomes one angle of the bigger triangle — then a right-triangle step finds a height.