Heights and Distances
- Line of sight is the line drawn from the eye of the observer to the point on the object viewed by the observer.
- Horizontal level is the horizontal line through the eye of the observer.
Angle of elevation
- The angle of elevation is relevant for objects above horizontal level.
- It is the angle formed by the line of sight with the horizontal level.
How to convert the above figure into the right triangle?
Case I: Angle of Elevation is known
Draw PQ perpendicular to RQ.
Now ∠RQP = 90°
ΔRQP is a rt. Δ, where
PR = hypotenuse
RQ = opposite side (Perpendicular)
PQ = adjacent side (Base)
Angle of depression
- The angle of depression is relevant for objects below horizontal level.
- It is the angle formed by the line of sight with the horizontal level.
How to convert the above figure into the right triangle?
Case II: Angle of Depression is known
(i) Draw DC parallel to AB
(ii) Draw perpendicular AD on DC.
(iii) Now ∠BAC = ∠ACD = Interior alternate angles
ΔADC is an rt. Δ. where
AC = hypotenuse
CD = adjacent side (base)
AD = opposite side (Perpendicular)
Calculating Heights and Distances
To, calculate heights and distances, we can make use of trigonometric ratios.
Step 1: Draw a line diagram corresponding to the problem.
Step 2: Mark all known heights, distances and angles and denote unknown lengths by variables.
Step 3: Use the values of various trigonometric ratios of the angles to obtain the unknown lengths from the known lengths.
- Choose a trigonometric ratio in such a way that it considers the known side and the side that you wish to calculate.
- The eye is always considered at ground level unless the problem specifically gives the height of the observer.