AB and CD of the base of the trapezoid, angle ABC = 63 ° angle CDA = 132 ° AB = 85mm BC = 51 mm.

| July 2, 2021 | education

AB and CD of the base of the trapezoid, angle ABC = 63 ° angle CDA = 132 ° AB = 85mm BC = 51 mm. Calculate AD, CD and AC diagonal.

The length of the diagonal AC is determined from the triangle ABC by the cosine theorem.

AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * Cos63 = 7225 + 2601 – 2 * 85 * 51 * Cos63 = 9826 + 8670 * 0.45 = 18496.45.

AC ≈ 136 mm.

Let’s draw the height of the CH. Then Sin63 = CH / BC. CH = BC * Sin63 = 51 * 0.89 = 45.39 mm.

Determine the length of the segment BH. BH = CB * Cos63 = 51 * 0.45 = 22.95 mm.

Let’s draw the height DK. Angle DAK = 180 – 132 = 48. Then AD = DK / Sin48 = 45.39 / 0.74 = 61.34 mm.

AK = AD * Cos48 = 61.34 * 0.67 = 41.1 mm.

Segment DC = KH = AB – AK – BH = 85 – 41.1 – 22.95 = 20.95 mm.

Answer: AC = 136 mm, AD = 61.34 mm, DC = 20.95 mm.



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