In Fig. 12.58, what are the angles of depression from the observing positions O₁ and O₂ of the object at A?

Question

In Fig. 12.58, what are the angles of depression from the observing positions O 1 and O 2 of the object at A?

Philoid · Accepted Answer

Let x be the angle of depression of object A from the point O₂

And y be the angle of depression of object A from the point O₁

In Δ AO₁C

∠O₁AC + ∠AC O₁ + ∠ACO₁ = 180° (angle sum property)

∠O₁AC + 90° + 60° = 180°

∠O₁AC = 30°

Through O₁ , draw O₁M ∥ AC

And through O₂ draw O₂N∥ AC

Now O₁M ∥ AC and AO₁ is transversal

∴ ∠O₁AC = y = 30° = ∠MO₁A (vertically opposite ∠s)

Similarly, O₂N∥ AC and AO₂ is transversal

∠NO₂ A = x = 45° = ∠O₂ AB (vertically opposite angles)

∴ Angles of depression are 30° and 45°