In Fig. 12.58, what are the angles of depression from the observing positions O1 and O2 of the object at A?
Answers
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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The angles of depression from the observing positions of and are 30° and 45°
Explanation:
Let x be the angle of depression of the object at A from point
Let y be the angle of depression of the object at B from point
Let us consider the triangle
By angle sum property, we have,
Let us draw a line parallel to AC
Also, let us draw a line parallel to AC
It is obvious that is a transversal line, then,
Also, is a transversal line, then,
Thus, the angles of depression from the observing positions of and 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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