In an isosceles trapezoid, the bases are 9cm and 15cm. Find the side of the trapezoid if the acute angle is 60 degrees.
| September 8, 2021 | education
From the top B of the trapezoid, draw the height BH. In an isosceles trapezium, the height drawn from the apex of an obtuse angle divides the larger base into two segments, the length of the smaller base is equal to the half-difference of the bases of the trapezoid.
AH = (AD – BC) / 2 = (15 – 9) / 2 = 6/2 = 3 cm.
In a right-angled triangle ABН, we determine the length of the hypotenuse AC.
CosBAN = AH / AB.
AB = AH / CosBAN = 3 / (1/2) = 3 * 2 = 6 cm.
Answer: The length of the side of the trapezoid is 6 cm.
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