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प्रश्न
Read the following passage:
A boy is standing on the top of light house. He observed that boat P and boat Q are approaching the light house from opposite directions. He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°. He also knows that height of the light house is 100 m.
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Based on the above information, answer the following questions.
- What is the measure of ∠APD?
- If ∠YAQ = 30°, then ∠AQD is also 30°, Why?
- Find length of PD
OR
Find length of DQ
उत्तर
i. XY || PQ and AP is transversal.
∠APD = ∠PAX ...(Alternative interior angles)
∠APD = 45°
ii. Since XY || PQ and AQ is a transversal
So alternate interior angles are equal
Hence ∠YAQ = ∠AQD = 30°
iii. In ΔADP, θ = 45°
tan θ = `"P"/"B"`
tan 45° = `100/("PD")`
PD = 100 m
Boat P is 100 m from the light house
OR
In ΔADQ, θ = 30°
tan θ = `"P"/"B"`
tan 30° = `100/("DQ")`
`1/sqrt(3) = 100/("DQ")`
DQ = `100sqrt(3)` m
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