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 16°18'. When the boat stops, the angle of depression is 48°51'. 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

@phi Please help.

Answer 2

I have no clue where to start.

Answer 3

did you draw a picture?

Answer 4

Yes, but I don't know whether to use Sin Cos, or Tan.

Answer 5

let's see the picture

Answer 6

Is that right?

Answer 7

yes, but I would make the 16 degrees 18 minutes into 16+18/60 degrees (60 min in 1 degree). that makes it 16.3 degrees

can you change 48 deg 51 mins to just degrees?

Answer 8

48 + 51 / 60 degrees so 1.65.

Answer 9

1.65? try again

Answer 10

it is (almost) like change hours and minutes to hours

Answer 11

How did you do it?

Answer 12

Oh! I understand, it's 48 + (51/60)

Answer 13

it is 48 degrees + a fraction of a degree 51/60

Answer 14

48.85

Answer 15

51/60=0.85 degrees
Total 48.85 degrees.

Answer 16

every 60 minutes is one deg

Answer 17

OK, now that you have the correct angles. How to pick the right trig function


which 2 legs are we going to use? 1) the one we know is a good choice
2) the leg we want to solve for is also a good choice

what trig function uses those 2 legs?

Answer 18

We know we have the opposite, and we want to know the adjecant. So we should use the tan.

Answer 19

yes.

now this is a two step problem because they want to know