Question

The sides of a parallelogram are 40 and 70 feet long,and the smaller angle has a measure of 36.Find the length of the longer diagonal to the nearest whole number

Answer 1

105 feet.

Explanation:

The longer diagonal is opposite the longer angle in the parallelogram.

The longer angle = 180 - 36 = 144 degrees. (Reason: he same side angles are supplementary).

So, by the law of cosines:

x^ 2 = 40^2 + 70^2 - 2*40*70 cos 140 where x = the diagonal.

x^2 = 11030.50

x = 105.03 feet.