SOLUTION: A rain gutter is 10 feet long. Its cross section is a trapezoid with an upper base of 5 inches and a lower base of 3 inches. The angle between the leg of the trapezoid and the lo

Question 1103252: A rain gutter is 10 feet long. Its cross section is a trapezoid with an upper base of 5 inches and a lower base of 3 inches. The angle between the leg of the trapezoid and the longer base is 78 degrees. Determine the volume of water the gutter can hold when completely filled with water. Express your answer using inches
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the trapezoid is presumably an isosceles trapezoid.
this means both legs are the same length.
if the lower base is 3 inches and the upper base is 5 inches, this means that the upper base extend 2 more inches on each side of the height of the trapezoid.
this forms a right triangle where the base is 1 inch and the base angle is 78 degrees.
you can find the length of the height by taking tan(78) = height / base.
solve for the height to get height = base * tan(78) = 1 * tan(78) = 4.704630109 inches.
area of the trapezoid is 1/2 * height * (b1 + b2) = 1/2 * 4.704630109 * 8 = 18.81852044 square inches.
volume of the gutter is length of the gutter times the area of the trapezoid = 120 * 18.81852044 = 2258.222453 cubic inches.
here's my picture.
not the best picture in the world, but hopefully good enough to show you what i mean.
$$$

here is also a link to an online calculator that you can use to check your work.
https://www.easycalculation.com/area/volume-of-trapezoidal-prism.php

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