anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
x1= 200/ tan 17°44' = .. x2 = 200/ tan 48°13' = ... The distance it traveled: x₁ - x₂ = ...
FireKat97
  • FireKat97
|dw:1442888207816:dw| You want to find x
FireKat97
  • FireKat97
|dw:1442888438629:dw| Start by finding theta and using theta find y

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More answers

anonymous
  • anonymous
how would i find theta?
anonymous
  • anonymous
would it be 90 - 48°13'
anonymous
  • anonymous
@FireKat97
anonymous
  • anonymous
im so lost
anonymous
  • anonymous
B = theta + 48°13'
FireKat97
  • FireKat97
Yup theta is correct sorry I marked beta wrong its |dw:1442888983577:dw|
FireKat97
  • FireKat97
so, now that you have theta, and you're already given one side, you can find y using trig
anonymous
  • anonymous
how? like which theorem?
FireKat97
  • 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
  • anonymous
sin
anonymous
  • anonymous
y/200
anonymous
  • anonymous
jk
anonymous
  • anonymous
tan, y/200
FireKat97
  • FireKat97
yup thats right
FireKat97
  • FireKat97
so y = ?
anonymous
  • anonymous
it is y=0.36397023
anonymous
  • anonymous
jk tan(1/200)y)
FireKat97
  • FireKat97
umm actually by using tan, we get; tanø = y/200 so y = 200.tanø
FireKat97
  • FireKat97
do you see why?
anonymous
  • anonymous
ohh ok yes
FireKat97
  • FireKat97
yup, and you know what theta is, you had it right before, so sub theta in, to find y.
anonymous
  • anonymous
y = 200.tan(90 - 48°13')
FireKat97
  • FireKat97
yes thats correct! now, we can apply the same techniques, to find z, tell me what you get for z
anonymous
  • anonymous
do i use B
FireKat97
  • FireKat97
yup, use beta
anonymous
  • anonymous
B = theta + 48°13'
anonymous
  • anonymous
B = (90 - 48°13')+ 48°13'
FireKat97
  • FireKat97
hang on, use this diagram|dw:1442890296933:dw|
FireKat97
  • FireKat97
|dw:1442890336639:dw|
FireKat97
  • FireKat97
hopefully thats clearer
FireKat97
  • FireKat97
so can you see how you would resolve for beta?
anonymous
  • anonymous
not really ;(
anonymous
  • anonymous
like what formula should i use
anonymous
  • anonymous
beta = 90 - 48°13'
FireKat97
  • FireKat97
beta = 90 - 17 degrees 44 minutes
FireKat97
  • FireKat97
do you see why?
FireKat97
  • FireKat97
My diagrams are really bad hahah sorry about that
anonymous
  • anonymous
sorry i took so long to respond!
anonymous
  • anonymous
@FireKat97
anonymous
  • anonymous
tan(z/200) = beta = tan(z/200)= 90- 17 degrees 44 minutes
anonymous
  • anonymous
y=449.20
FireKat97
  • 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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