Final answer:
To find the height of the trapezoid-shaped cross section of the water bin, use the area formula for a trapezoid which yields a height of 3 feet.
Step-by-step explanation:
The cross section of a water bin is shaped like a trapezoid with bases of 17 feet and 3 feet, and its area is 30 square feet. To find the height of the trapezoid, we can use the formula for the area of a trapezoid, which is A = (1/2) * (b1 + b2) * h, where A is the area, b1 and b2 are the lengths of the bases, and h is the height.
The formula can be rearranged to solve for the height (h): h = 2A / (b1 + b2). Substituting the given values:
h = 2 * 30 sq ft / (17 ft + 3 ft)
h = 60 sq ft / 20 ft
h = 3 feet
Therefore, the height of the cross section of the water bin is 3 feet.