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 16° 23'. When the boat stops, the angle of depression is 49° 29'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round to the nearest hundredth.

Question

anonymous · Answer

@campbell_st do you have any idea for this one??:(

jim_thompson5910 · Answer

16° 23' = 16 + 23/60 degrees

16° 23' = 16 + 0.3833 degrees

16° 23' = 16.3833 degrees



49° 29'= 49 + 29/60 degrees

49° 29' = 49 + 0.4833 degrees

49° 29' = 49.4833 degrees


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jim_thompson5910 · Answer

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jim_thompson5910 · Answer

the goal is to find y

but you first need to find x

anonymous · Answer

x i got 170!

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

I'm getting 170.91697897468

is that what you got?

anonymous · Answer

yes!

jim_thompson5910 · Answer

ok now use this to find y

anonymous · Answer

how?? O.o

jim_thompson5910 · Answer

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jim_thompson5910 · Answer

tan(16.3833) = opp/adj

tan(16.3833) = 200/(170.91698 + y)

solve for y

anonymous · Answer

ohhh i got 509 @jim_thompson5910

jim_thompson5910 · Answer

I'm getting around 509.3567143

so congrats