• anonymous
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed the angle of depression to the boat is 16° 23'. When the boat stops, the angle of depression is 49° 29'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round to the nearest hundredth.
  • Stacey Warren - Expert
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  • schrodinger
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  • anonymous
This is not difficult. Use the tangent function of each angle. tan Θ = height of lighthouse / distance of boat from lighthouse. tan (15.85°) = 200 / x x = 200 / tan 15.85° x ≈ 704.438 ft tan (52.2°) = 200 / x' x' = 200 / tan (52.2°) x' ≈ 155.136 ft.. The distance the boat traveled is equal to x - x': x - x' = 704.438 ft - 155.136 ft = 549.302 ft. We can then round the answer to 549.30 ft.|dw:1355174045554:dw|
  • anonymous
got it thanksssss :)
  • radar

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