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Question
From the top of a lighthouse, an observer looking at a ship makes angle of depression of 60°. If the height of the lighthouse is 90 metre, then find how far the ship is from the lighthouse.
Solution
Let AB be the lighthouse and C be the position of the ship from the lighthouse.
Suppose the distance of the ship from the lighthouse be x m.
In right ∆ABC,
\[\tan60^\circ = \frac{AB}{BC}\]
\[ \Rightarrow \sqrt{3} = \frac{90}{x}\]
\[ \Rightarrow x = \frac{90}{\sqrt{3}} = 30\sqrt{3}\]
\[ \Rightarrow x = 30 \times 1 . 73 = 51 . 9 m\]
Thus, the ship is 51.9 m away from the lighthouse.
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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
