SOLUTION: 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�31'. When th

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Question 628648: 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�31'. When the boat stops, the angle of depression is 46�41'. 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 by ankor@dixie-net.com(22740) (Show Source):
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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�31'.
When the boat stops, the angle of depression is 46�41'.
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.
:
Change 17 degrees 31 minutes to 17 + 31/60 = 17.5167 degrees
Change 46 degrees 41 minutes to 46.6833 degrees
:
We can solve this using two right triangles
90 - 17.5167 = 72.4833
Side opposite will be distance (D) from the lighthouse to the boat when noticed
Side adjacent: the lighthouse; 200 ft
tan(72.4833) =
D = 3.16837 * 200
D = 633.675 ft, lighthouse to boat when noticed
:
The 2nd right triangle:
90 - 46.6833 = 43.3167
side opposite will be distance (d) from lighthouse to boat when it stopped
tan(43.3167) =
d = .9429 * 200
d = 188.580 ft, lighthouse to boat it stopped
:
Boat traveled: 633.675 - 188.580 = 445.09 ft