Question 1173500: A Carpenter Is Building A Structure In The Shape Of An Isosceles Trapezoid Whose Base Angles Measure 60 Degree. The base of the trapezoid has a length of 25 fett., while the legs of the trapezoid have the lengths of 12 feet. The carpenter would like to by stabalize the trapezpoid by placing support beams along the diagnols of the trapezoid at a cost of $2.50 per linear foot. Determine the combined cost of the diagnols to the nearest dollar.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Picture dividing the trapezoid into a rectangle and two 30-60-90 right triangles.
In each of the 30-60-90 right triangles, the hypotenuse is 12, so the base is 6 and the height is 6*sqrt(3).
With the base of each triangle being 6, the width of the rectangle is 25-2(6)=13.
Each diagonal of the trapezoid is then the hypotenuse of a right triangle with legs 13+6=19 and 6*sqrt(3).
Use the Pythagorean Theorem to calculate the length of each diagonal.
Then multiply the total length of the two diagonals by the given cost per foot and round the answer to the nearest dollar, as instructed.
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