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 14°52'. When the boat stops, the angle of depression is 45°10'. 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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dschneider2016 · Answer

Please help!! Will medal!!

dschneider2016 · Answer

@Photon336

photon336 · Answer

We represent X_{1} the position where the boat is originally at. theta 1 is the angle that it makes, i.e. the angle of depression and 200 is the height of the boat. 

we want to represent the two fro both of them. where the boat is at position one and where it is at position two. but we don't know these things. we need to find them.

$$x_{1} = 200Cot(\theta_{1})$$

we represent the same for X_{2} 

$$X_{2} = 200Cot(\theta_{2})$$

we need to find where the boat is or how far it traveled, so that would be displacement I believe (x2-x1)


$$x_{1}-x_{2} = 200Cot(\theta_{1}-\theta_{2})$$

photon336 · Answer

then we plug in our values, BTW i PUT these into my calculator Cot = cotangent, 

$$200(\cot(14+52/60)-\cot(45+10/60))$$

photon336 · Answer

so this would give us 554.58 rounded to the hundreds place. i'll try to draw out a figure for you too. I think this is how you would do this.

dschneider2016 · Answer

Thank you so much!! This is so helpful!

photon336 · Answer

Not a problem