Math, asked by Navie4321, 11 months ago

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

Answers

Answered by amitnrw
7

angle of depression from the observing positions O₁  = 30° & angle of depression from the observing positions O₂  =  45°

Step-by-step explanation:

See the attached  Figure

angle of depression from the observing positions O₁  = 90° - 60°

=> angle of depression from the observing positions O₁  = 30°

∠A = 45°

=> ∠AO₂B = 90⁰ - 45⁰ = 45⁰

=> ∠AO₂B = 45⁰

angle of depression from the observing positions O₂  = 90° - 45°

= 45°

angle of depression from the observing positions O₂  =  45°

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Attachments:
Answered by adventureisland
5

The angles of depression from the observing positions of O_1 and O_2 are 30° and 45°

Explanation:

Let x be the angle of depression of the object at A from point O_1

Let y be the angle of depression of the object at B from point O_2

Let us consider the triangle Q_1CA

By angle sum property, we have,

\angle \mathrm{O}_{1} \mathrm{AC}+\angle \mathrm{ACO}_{1}+\angle \mathrm{AO}_{1} \mathrm{C}=180^{\circ}

             \angle \mathrm{O}_{1} \mathrm{AC}+90^{\circ}+60^{\circ}=180^{\circ}

                     \angle \mathrm{O}_{1} \mathrm{AC}+150^{\circ}=180^{\circ}

                                 \angle \mathrm{O}_{1} \mathrm{AC}=30^{\circ}

Let us draw a line \mathrm{O}_{1} \mathrm{M} parallel to AC

Also, let us draw a line \mathrm{O}_{2} \mathrm{N} parallel to AC

It is obvious that \mathrm{O}_{1} \mathrm{A} is a transversal line, then,

\ {x}=\angle \mathrm{O}_{1} \mathrm{AC}

x=30^{\circ}

Also, \mathrm{O}_{2} \mathrm{A} is a transversal line, then,

\ y=\angle \mathrm{O}_{2} \mathrm{AB}

y=45^{\circ}

Thus, the angles of depression from the observing positions of O_1 and O_2 are 30° and 45°

Learn more:

(1) A person observes two banks of a river at angles of depression theta 1 and theta 2(theta 1<theta 2) from the top of a tree of height h which is at a side of the river.The width of the rivers is d.Draw the diagram for given situation.​

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(2) From the top of a hill 200m high, the angles of depression of the top and the bottom of a pillar are 30°and 60° respectively. Find the height of the pillars and uts distance from the hill.

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