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Question
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Case Study Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. |
- Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
- After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?
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Solution
i.
In ∆PTR, tan 30° = `240/x` ⇒ x = `240sqrt(3)` m
ii. Distance of boat from tower = `240sqrt(3) - 240(sqrt(3) - 1)` = 240 m
Let the angle of depression = θ
tan θ = `240/240` = 1 ⇒ θ = 45°
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