Q. 6

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

Answer :

Let x be the angle of depression of object A from the point O_{2}

And y be the angle of depression of object A from the point O_{1}

In Δ AO_{1}C

∠O_{1}AC + ∠AC O_{1} + ∠ACO_{1} = 180° (angle sum property)

∠O_{1}AC + 90° + 60° = 180°

∠O_{1}AC = 30°

Through O_{1} , draw O_{1}M ∥ AC

And through O_{2} draw O_{2}N∥ AC

Now O_{1}M ∥ AC and AO_{1} is transversal

∴ ∠O_{1}AC = y = 30° = ∠MO_{1}A (vertically opposite ∠s)

Similarly, O_{2}N∥ AC and AO_{2} is transversal

∠NO_{2} A = x = 45° = ∠O_{2} AB (vertically opposite angles)

∴ Angles of depression are 30° and 45°

Rate this question :

If θ = 45°, find the value of

(i)

(ii) cos^{2} θ - sin^{2} θ

Find the numerical value of the following :

sin45°.cos45° – sin^{2}30°.

At a point A, 20 meters above the level of water in a lake, the angle of elevation of a cloud is 30°. The angle of depression of the reflection of the cloud in the lake, at A is 60°. Find the distance of the cloud from A.

Mathematics - Board PapersEvaluate each of the following:

RD Sharma - MathematicsIf , where and are acute angles, find the value of .

RD Sharma - MathematicsEvaluate the following :

cosec^{2}30°.tan^{2}45° – sec^{2}60°