SOLUTION: The angle of elevation from buoys C and D to the top of a cliff AB is 40 degrees and 30 degrees respectively. If Ross swims from C to D with a constant speed of 1.5m/s and AC=100m,
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Question 1098356: The angle of elevation from buoys C and D to the top of a cliff AB is 40 degrees and 30 degrees respectively. If Ross swims from C to D with a constant speed of 1.5m/s and AC=100m, find the distance between the two buoys.
Any help is greatly appreciated!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the triangles formed are ABC and ABD.
angle ACB is equal to 40 degrees.
angle ADB is equal to 30 degrees.
tan(40) = opposite / adjacent = AB / AC.
since AC = 100, this becomes tan(40) = AB / 100
solve for AB to get AB = 100 * tan(40) = 83.90996312
tan(30) = opposite / adjacent = AB / AD.
since AB is equal to 83.90996312, this becomes tan(30) = 83.90996312 / AD.
solve for AD to get AD = 83.90996312 / tan(30) = 145.3363194
since AD = AC + CD, then you get 145.3363194 = 100 + CD.
solve for CD to get CD = 145.3363194 - 100 = 45.3363194.
CD is the distance between the two buoys.
not sure where the speed comes in.
if the distance from A to C is 100 meters and ross swims at 1.5 meters per second, then it takes him 100 / 1.5 = 66.6666667 seconds to swim from A to C.
if he continues to swim at the same rate, then it takes him 45.3363194 / 1.5 = 30.22421292 seconds to swim buoy C to buoy D.
the total time it takes is 145.3363194 / 1.5 = 96.89087959 seconds to swim from the bottom of the cliff to buoy D.
to me, the speed at which he swam was irrelevant to the problem since you didn't need it to find the distance between buoy C and C.
here's the diagram i drew of the problem.
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