## 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? one year ago one year ago

1. JakeV8 Group Title

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 Group Title

I still don't get it.

3. JakeV8 Group Title

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 Group Title

5. JakeV8 Group Title

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 Group Title

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

7. JakeV8 Group Title

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 Group Title

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

9. Caolco Group Title

10. swissgirl Group Title

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

11. Caolco Group Title

so the answer is -706.44 ft

12. swissgirl Group Title

noooo did you solve this?

13. swissgirl Group Title

How can distance be negative?

14. Caolco Group Title

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 Group Title

Are you on radians or degrees?

16. swissgirl Group Title

You must be on radians switch the mode to degrees

17. Caolco Group Title

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

18. swissgirl Group Title

Yesss :)

19. JakeV8 Group Title

@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.