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?

1. JakeV8

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. Caolco

I still don't get it.

3. JakeV8

I messed up the labeling above... it is 51 deg 33 min and 18 deg 33 min (I put "sec" in for both)

4. swissgirl

5. JakeV8

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)

6. Caolco

do I divide 200 by tan(18+33/60)-tan(51+33/60)?

7. JakeV8

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

8. JakeV8

I'm not sure... why would you divide it by the difference in those two tangents?

9. Caolco

10. swissgirl

$$\large {200 \over \tan(18+{33 \over 60}) }-{200 \over\tan(51+{33 \over 60})}$$

11. Caolco

so the answer is -706.44 ft

12. swissgirl

noooo did you solve this?

13. swissgirl

How can distance be negative?

14. Caolco

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.

15. swissgirl

Are you on radians or degrees?

16. swissgirl

You must be on radians switch the mode to degrees

17. Caolco

oh pellet. i changed it to degrees before doing this but must not have hit enter. damnit. is the answer 437.21?

18. swissgirl

Yesss :)

19. JakeV8

@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.