# Tan

• Oct 14th 2012, 03:53 PM
akldfj
Tan
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 18°33'. When the boat stops, the angle of depression is 51°33'. 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.

• Oct 14th 2012, 04:28 PM
MaxJasper
Re: Tan
Let me know if 596.01' - 158.8' = 437.21' is correct.
• Oct 14th 2012, 04:29 PM
akldfj
Re: Tan
Yes it is.
• Oct 14th 2012, 04:39 PM
akldfj
Re: Tan
• Oct 14th 2012, 04:45 PM
MaxJasper
Re: Tan
$\frac{200}{\tan \left(18\text{ }33'\right)}-\frac{200}{\tan \left(51\text{ }33'\right)}$
• Oct 14th 2012, 04:49 PM
akldfj
Re: Tan
so I divide 200 by tan(18+33/60)-tan(51+33/60)

Is that right?
• Oct 14th 2012, 04:57 PM
akldfj
Re: Tan
So the answer is -706.44 ft?
• Oct 14th 2012, 05:10 PM
MaxJasper
Re: Tan