Question

Construct a trapezium ABCD such that AD is parallel to BC, AB = 4.8 cm, BC = 6.8 cm, CD = 5.4 cm and ∠ABC = 60°. Measure and write down the length of AC.

Answer 1

AC = 6.05 cm

Explanation:

We can draw two different trapeziums with the information given.

The possible drawings of the trapezium ABCD are in the image attached.

In both trapeziums, the length of AC is the same, and we can calculate this length using the law of cosines in the triangle ABC:

AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(B)

AC^2 = 4.8^2 + 6.8^2 - 2 * 4.8 * 6.8 * cos(60)

AC^2 = 23.04 + 46.24 - 65.28 * 0.5

AC^2 = 36.64

AC = 6.05 cm