Question 901783: A submarine captain discovered that his depth gauge was broken. To determine his depth, he used his sonar to find
that he was directly between two ships on the surface. From the sub to one ship there was an angle of elevation of
51.27°, while the angle of elevation to the other ship was 13.9°. What was the depth of the sub if the two ships were
5000 feet apart?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A submarine captain discovered that his depth gauge was broken. To determine his depth, he used his sonar to find
that he was directly between two ships on the surface. From the sub to one ship there was an angle of elevation of
51.27°, while the angle of elevation to the other ship was 13.9°. What was the depth of the sub if the two ships were
5000 feet apart?
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Draw the picture. Let the depth be "d". Parts of the distance are x and 5000-x.
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Equation::
tan(38.73) = (5000-x)/d
tan(76.1) = x/d
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Work the algebra to solve for "x":
x = (5000*tan(76.1))/(tan(38.73)+tan(76.1)
x = 20204/4.84
x = 4172 ft
5000-x = 828 ft
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Comment:: Now you can solve for "d".
Cheers,
Stan H.
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