Question 626466: he captain of a ship wants to determine his distance from shore. Seeking a familiar landmark, he finds a 90-ft-high lighthouse on top of a cliff. He sights both the top and bottom of the lighthouse. The measures of the two angles of elevation are 46 and 39. How far, to two significant digits, is he from the base of the cliff?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! he captain of a ship wants to determine his distance from shore. Seeking a familiar landmark, he finds a 90-ft-high lighthouse on top of a cliff. He sights both the top and bottom of the lighthouse. The measures of the two angles of elevation are 46 and 39. How far, to two significant digits, is he from the base of the cliff?
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Draw a right triangle with the vertical leg=90+y, y=height of the cliff.
And horizontal leg=x, distance from ship to base of the cliff.
..
tan 46º=(90+y)/x
x=tan 46º*(90+y)
..
tan 39º=y/x
y=xtan39º
..
tan 46º=(90+xtan39º)/x
xtan46º=90+xtan39º
xtan46º-xtan39º=90
x(tan46º-tan39º)=90
x=90/(tan46º-tan39º)
x≈398.68 ≈400 ft
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