In trapezoid ABCD (BC – smaller base) diagonal AC = 4 cm, larger base is 8 cm, angle ABC = 110 °

univerkov | May 13, 2021 | education

In trapezoid ABCD (BC – smaller base) diagonal AC = 4 cm, larger base is 8 cm, angle ABC = 110 °, angle BAC = 30 °. find the side of the CD.

The sum of the angles of a trapezoid at its lateral side is 180.

Then the angle (ABC + BAC + CAD) = 180.

(110 + 30 + CAD) = 180.

Angle CAD = 180 – 110 – 30 = 40.

In the triangle ACD, we apply the cosine theorem and determine the length of the side CD.

CD ^ 2 = AC ^ 2 + AD ^ 2 – 2 * AC * AD * CosA = 16 + 64 – 2 * 4 * 8 * Cos40 = 80 – 64 * 0.766 = 30.976.

CD ≈ 5.57 cm.

Answer: The length of the CD side is 5.57 cm.

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