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Caolco Group Title

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 18°33'. When the boat stops, the angle of depression is 51°33'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place. Is the answer -706.44 ft?

  • 2 years ago
  • 2 years ago

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  1. JakeV8 Group Title
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    I don't know the answer yet, but this diagram should help. Also, when you calculate a distance traveled, it will always be expressed as a positive number. |dw:1350260299986:dw|

    • 2 years ago
  2. Caolco Group Title
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    I still don't get it.

    • 2 years ago
  3. JakeV8 Group Title
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    I messed up the labeling above... it is 51 deg 33 min and 18 deg 33 min (I put "sec" in for both)

    • 2 years ago
  4. swissgirl Group Title
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    Well what dont u get? what exactly is bothering you about this diagram?

    • 2 years ago
  5. JakeV8 Group Title
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    you could solve for the total distance from the boat's initial position to the lighthouse base using tangent(18 +33/60) = 200 ft / (entire base distance)

    • 2 years ago
  6. Caolco Group Title
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    do I divide 200 by tan(18+33/60)-tan(51+33/60)?

    • 2 years ago
  7. JakeV8 Group Title
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    and you could do the same for the other angle to get the distance from the point where the boat stopped back to the lighthouse. Then subtract to get the distance travelled

    • 2 years ago
  8. JakeV8 Group Title
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    I'm not sure... why would you divide it by the difference in those two tangents?

    • 2 years ago
  9. Caolco Group Title
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    i don't know. can you please just give me the answer?

    • 2 years ago
  10. swissgirl Group Title
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    \( \large {200 \over \tan(18+{33 \over 60}) }-{200 \over\tan(51+{33 \over 60})} \)

    • 2 years ago
  11. Caolco Group Title
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    so the answer is -706.44 ft

    • 2 years ago
  12. swissgirl Group Title
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    noooo did you solve this?

    • 2 years ago
  13. swissgirl Group Title
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    How can distance be negative?

    • 2 years ago
  14. Caolco Group Title
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    yes and that is what i keep getting. that is the exact way i did it the first time and that is the same answer im getting now.

    • 2 years ago
  15. swissgirl Group Title
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    Are you on radians or degrees?

    • 2 years ago
  16. swissgirl Group Title
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    You must be on radians switch the mode to degrees

    • 2 years ago
  17. Caolco Group Title
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    oh pellet. i changed it to degrees before doing this but must not have hit enter. damnit. is the answer 437.21?

    • 2 years ago
  18. swissgirl Group Title
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    Yesss :)

    • 2 years ago
  19. JakeV8 Group Title
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    @Caolco sorry, it took me awhile to even see how to solve this, then, since I apparently needed the practice, I was trying to solve it while @swissgirl was helping you.

    • 2 years ago
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