The area of a rectangular trapezoid ABCD is 44, and its base is 7 and 15, find the tangent of the acute angle of the trapezoid.
| July 10, 2021 | education
From the vertex C we will construct the height CH of the trapezoid ABCD.
From the formula for the area of the trapezoid, we express the height CH of the trapezoid.
Savsd = (BC + AD) * CH / 2.
H = 2 * Savsd / (BC + AD) = 2 * 44 / (7 + 15) = 88/22 = 4 cm.
Quadrangle ABCН is a rectangle, then AH = BC = 7 cm.
Then DH = AD – AH = 15 – 7 = 8 cm.
The CDH triangle is rectangular, then tgCDH = CH / DH = 4/8 = 1/2 = 0.5.
Answer: The tangent of the acute angle of the trapezoid is 0.5.
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