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.

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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
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x1= 200/ tan 17°44' = .. x2 = 200/ tan 48°13' = ... The distance it traveled: x₁ - x₂ = ...
|dw:1442888207816:dw| You want to find x
|dw:1442888438629:dw| Start by finding theta and using theta find y

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