Question

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.

Based on the above information, answer the following questions.

1. What is the measure of ∠APD?
2. If ∠YAQ = 30°, then ∠AQD is also 30°, Why?
3. Find length of PD
   OR
   Find length of DQ

Answer 1

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