Question

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 13°7'. When the boat stops, the angle of depression is 50°42' . 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.

Answer 1

help!!!!!!!!!!!!

Answer 2

what you want to find is the value of y in the diagram above

Answer 3

yes!

Answer 4

first convert each angle measure

50 degrees 42 min = 50 + 42/60 degrees

50 degrees 42 min = 50 + 0.7 degrees

50 degrees 42 min = 50.7 degrees

Answer 5

13 degrees 7 min = 13 + 7/60 degrees

13 degrees 7 min = 13 + 0.11667 degrees

13 degrees 7 min = 13.11667 degrees

Answer 6

so we get this

Answer 7

the first step is to solve for x

how do we do this?

Answer 8

sin(50.7)=200/x
so x=258.45?!?!

Answer 9

@jim_thompson5910

Answer 10

tan(angle) = opposite/adjacent

tan(50.7) = 200/x

x*tan(50.7) = 200

x = 200/tan(50.7)

x = ???

Answer 11

make sure you're in degree mode

Answer 12

umm i got 163.698!

Answer 13

me too

Answer 14

so x is roughly x = 163.698

Answer 15

now we can find y with this info

Answer 16

tan(angle) = opposite/adjacent

tan(13.11667) = 200/(x + y)

tan(13.11667) = 200/(163.698 + y)

0.233014 = 200/(163.698 + y)

0.233014(163.698 + y) = 200

I'll let you finish

Answer 17

@jim_thompson5910 ohh so y=161.856 ?

Answer 18

no it's a bit small

Answer 19

@jim_thompson5910 is it 694.62??

Answer 20

much better

Answer 21

I'm getting 694.6195260, and that rounds to 2 places to get 694.62

Answer 22

@jim_thompson5910 yeahh!!:) so 694.62 will the answer right?

Answer 23

yes roughly

hopefully we used accurate enough versions of tan(13.11667) and tan(50.7)

but yes, 694.62 is pretty much it

Answer 24

okay! thank you!!!!!!!! :D

Answer 25

you're welcome