The base of an isosceles trapezoid is 12 and 30. The sine of one of the corners of the trapezoid is 0.8. Find the side of the trapezoid.
Let’s build the height BH of the trapezoid ABCD. Since the trapezoid is isosceles, the height BH divides the base of AD into two segments, the length of the smaller of which is equal to the half-difference of the lengths of the bases.
AH = (AD – BC) / 2 = (30 – 12) / 2 = 9 cm.
In a right-angled triangle ABH SinA = 0.8 = AH / AB.
AB = AH / SinA = 9 / 0.8 = 11.25 cm.
Answer: The side of the trapezoid is 11.25 cm.
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