SOLUTION: A scuba diver plans a brief expedition to swim out to a buoy located 90 feet fron the shore.the diver who is 5 feet tall can be totally submerged ubdervthe water 12 feet from the s

Question 1010387: A scuba diver plans a brief expedition to swim out to a buoy located 90 feet fron the shore.the diver who is 5 feet tall can be totally submerged ubdervthe water 12 feet from the shoreline horizontally if they walk 13 feet in a diagonal direction along the ocean floor.how deep is the water directly below the buoy?what is the total distance the scuba diver will travel if they swim from the shoreline to the buoy,then the buoy to the ocean bottom?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
assuming that the diagonal along the ocean floor continues all the way to the ocean floor beneath the buoy, you have two similar triangles formed.

the first triangle has a horizontal component of 12 feet and a vertical component of 5 feet and a diagonal component of 15 feet.

the second triangle has a horizontal component of 90 feet.

since the triangles are similar, their corresponding sides are proportional.

the vertical component would be found by the ratio of 12/5 = 90/x.

solve for x to get x = 90*5/12 = 37.5 feet.

the diagonal component would be found by the ratio of 12/13 = 90/y.

solve for y to get y = 90*13/12 = 97.5 feet.

the larger triangle, which includes the smaller triangle, is 90 by 37.5 by 97.5

the smaller triangle, which is contained in the larger triangle, is 12 by 5 by 13.

the triangle are proportional which means that the ratio between their corresponding sides is the same.

this means that 12/90 = 13/97.5 = 5/37.5

12/90 = .133333.....

13/97.5 = .133333.....

5/37.5 = .133333......

the ratios are the same so the triangles are similar.

the question is:

what is the total distance the scuba diver will travel if he swims from the shoreline to the buoy and then from the buoy to the ocean bottom.

that will be 90 + 37.5 = 127.5 feet.

the diagram for this problem is shown below:

in the diagram.
A is the shore.
C is the buoy.
D is the bottom of the water beneath the buoy.
B is the point where the diver is completely submerged.
E is the bottom of the water where the diver is completely submerged.

$$$

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