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Caolco
 2 years ago
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?
Caolco
 2 years ago
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?

This Question is Closed

JakeV8
 2 years ago
Best ResponseYou've already chosen the best response.1I 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

JakeV8
 2 years ago
Best ResponseYou've already chosen the best response.1I messed up the labeling above... it is 51 deg 33 min and 18 deg 33 min (I put "sec" in for both)

swissgirl
 2 years ago
Best ResponseYou've already chosen the best response.2Well what dont u get? what exactly is bothering you about this diagram?

JakeV8
 2 years ago
Best ResponseYou've already chosen the best response.1you 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)

Caolco
 2 years ago
Best ResponseYou've already chosen the best response.1do I divide 200 by tan(18+33/60)tan(51+33/60)?

JakeV8
 2 years ago
Best ResponseYou've already chosen the best response.1and 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

JakeV8
 2 years ago
Best ResponseYou've already chosen the best response.1I'm not sure... why would you divide it by the difference in those two tangents?

Caolco
 2 years ago
Best ResponseYou've already chosen the best response.1i don't know. can you please just give me the answer?

swissgirl
 2 years ago
Best ResponseYou've already chosen the best response.2\( \large {200 \over \tan(18+{33 \over 60}) }{200 \over\tan(51+{33 \over 60})} \)

Caolco
 2 years ago
Best ResponseYou've already chosen the best response.1so the answer is 706.44 ft

swissgirl
 2 years ago
Best ResponseYou've already chosen the best response.2noooo did you solve this?

swissgirl
 2 years ago
Best ResponseYou've already chosen the best response.2How can distance be negative?

Caolco
 2 years ago
Best ResponseYou've already chosen the best response.1yes 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.

swissgirl
 2 years ago
Best ResponseYou've already chosen the best response.2Are you on radians or degrees?

swissgirl
 2 years ago
Best ResponseYou've already chosen the best response.2You must be on radians switch the mode to degrees

Caolco
 2 years ago
Best ResponseYou've already chosen the best response.1oh pellet. i changed it to degrees before doing this but must not have hit enter. damnit. is the answer 437.21?

JakeV8
 2 years ago
Best ResponseYou've already chosen the best response.1@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.
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