One side of a parallelogram is 15 feet and another side is 14 feet. The angle between these two sides is 50degrees. Find the lengths of the diagonals to the nearest tenth of a foot.

Answer 1

I'm using a trig formula. a=14; b=15, c=?

To find side "c" (the diagonal) the formula is a^2+b^2-2ab(cosγ)=c^2.

In this case γ=180-55=125°.

((14^2+15^2)-(2*14*15)cos125)=c^2

((196+225)-420*-.574)^.5=25.73

γ=acos((a^2+b^2-c^2)/(2ab))

125=acos((14^2+15^2-c^2)/(2*14*15))

c=25.73

Answer 2

By the law of cosines, the first diagonal is:

d² = 14² + 15² - 2(14)(15)(cos 50°)

For the second diagonal, you first need to find the other angle of the parallelogram. Since consecutive angles of a parallelogram are supplementary, this angle is 130. Therefore, the other diagonal is:

c² = 14² + 15² - 2(14)(15)(cos 130°)

Answer 3

Draw and label a diagram!

Use the Law of Cosines

d² = 14² + 15² - 2(14)(15)(cos 50°)