The lengths of 2 adjacent sides of a parallelogram are 42 cm and 36cm. an angle of the parallelogram is 4o degrees. Find the measure of the longest diagonal to the nearest tenth of a centimeter.

Answer 1

The longest diagonal forms a triangle with 180°-40°=140° and adjacent sides of 42 and 36 cm.

Using the cosine rule:
C²=A²+B²-2ABcos(α)
=42²+36²-2*42*36*cos(140°)
=1764+1296-3024(-.766044443)
=5376.52 approx.
C=sqrt(5376.52)
=73.32 cm (approx.)