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 17°44'. When the boat stops, the angle of depression is 48°13' . 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.

- anonymous

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- anonymous

x1= 200/ tan 17°44' = ..
x2 = 200/ tan 48°13' = ...
The distance it traveled:
x₁ - x₂ = ...

- FireKat97

|dw:1442888207816:dw|
You want to find x

- FireKat97

|dw:1442888438629:dw| Start by finding theta and using theta find y

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## More answers

- anonymous

how would i find theta?

- anonymous

would it be 90 - 48°13'

- anonymous

@FireKat97

- anonymous

im so lost

- anonymous

B = theta + 48°13'

- FireKat97

Yup theta is correct
sorry I marked beta wrong its |dw:1442888983577:dw|

- FireKat97

so, now that you have theta, and you're already given one side, you can find y using trig

- anonymous

how? like which theorem?

- FireKat97

okay, so you have |dw:1442889317113:dw|
so you have the "adjacent" side and you're looking for the "opposite", according to
S-OH
C-AH
T-OA
which trig function do you think is best to use?

- anonymous

sin

- anonymous

y/200

- anonymous

jk

- anonymous

tan, y/200

- FireKat97

yup thats right

- FireKat97

so y = ?

- anonymous

it is y=0.36397023

- anonymous

jk tan(1/200)y)

- FireKat97

umm actually by using tan, we get;
tanø = y/200
so y = 200.tanø

- FireKat97

do you see why?

- anonymous

ohh ok
yes

- FireKat97

yup, and you know what theta is, you had it right before, so sub theta in, to find y.

- anonymous

y = 200.tan(90 - 48°13')

- FireKat97

yes thats correct! now, we can apply the same techniques, to find z, tell me what you get for z

- anonymous

do i use B

- FireKat97

yup, use beta

- anonymous

B = theta + 48°13'

- anonymous

B = (90 - 48°13')+ 48°13'

- FireKat97

hang on, use this diagram|dw:1442890296933:dw|

- FireKat97

|dw:1442890336639:dw|

- FireKat97

hopefully thats clearer

- FireKat97

so can you see how you would resolve for beta?

- anonymous

not really ;(

- anonymous

like what formula should i use

- anonymous

beta = 90 - 48°13'

- FireKat97

beta = 90 - 17 degrees 44 minutes

- FireKat97

do you see why?

- FireKat97

My diagrams are really bad hahah sorry about that

- anonymous

sorry i took so long to respond!

- anonymous

@FireKat97

- anonymous

tan(z/200) = beta
= tan(z/200)= 90- 17 degrees 44 minutes

- anonymous

y=449.20

- FireKat97

Sorry I was on the train ahaha.
I think we should take this slow, so we established that beta is 90 - 17* 44' right? Do you agree?

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