• anonymous
Find the angle of depression from the top of a lighthouse 250 feet above water level to the water line of a ship 2.5 miles offshore.
  • Stacey Warren - Expert
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  • chestercat
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  • Kainui
Consider your trigonometric functions, sine, cosine, and tangent. Do you know SOH CAH TOA? Try drawing out a picture, I'll help give an example: |dw:1328143919004:dw| So you see that you want the angle and you're given the height of the lighthouse and distance of the lighthouse from the ship. Where are the sides in relation to the angle? Are they opposite, adjacent, or the hypotenuse? You are given the opposite side to the angle and the one that's adjacent to the angle. This relates to TOA in SOH CAH TOA meaning Tangent of an angle is equal to the ratio of the opposite side to the adjacent side. \[\tan \theta=O/A\] Using simple algebra, just apply the inverse tangent function to both sides to get this: \[\theta=\tan^{-1}(O/A)\] and you can plug this into your calculator. Don't forget that the height of the lighthouse is in feet and the distance from the boat to the lighthouse is in miles, so you need to convert between the two. Remember, 1 mile =5280 ft Be careful about whether your calculator is set to radians or degrees for your "units"
  • anonymous
Thank you so much! You're a lifesaver!!!

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