SOLUTION: The vertical sidewall of an in-ground pool that is 24 ft in length has the shape of a right trapezoid. What is the depth of the pool in the middle Trapezoid ABCD with AD= 3 ft BC

Question 1084333: The vertical sidewall of an in-ground pool that is 24 ft in length has the shape of a right trapezoid. What is the depth of the pool in the middle
Trapezoid ABCD with AD= 3 ft BC= 13 ft AB= 24 ft
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it's 3 feet on the shallow end.
it's 13 feet on the deep end.
it's 24 feet at a vertical from the shallow end to the deep end.

the pool cross section is divided into 2 segments.

1 segment is a rectangle that has a length of 24 and a depth of 3.

the other segment is a right triangle that has a base of 24 and a depth of 10 at the deep end and a depth of 0 at the shallow end.

the angle formed from the shallow end to the deep end is equal to arctan(10/24) = 22.61986495 degrees.

split the base of the triangle in the middle and the base of that triangle is 12.

solve for the depth of that triangle and you start with tan(22.61986495) = x/12

solve for x to get x = 12 * tan(22.61986495) = 5.

since the smaller right triangle formed is similar to the larger right triangle formed, you could also solve as a proportion since all the angles are equal and therefore the sides are proportional.

you would get x/12 = 10/24

cross multiply to get 24x = 120

divide both sides by 24 to get x = 5

here's my diagram of what i think you were talking about.

$$$

your solution is that the depth in the middle is 3 + 5 = 8 feet.

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