Chapter 6, Problem 39CR

To determine

To find: the lengths of the sides of the parallelogram when the diagonals intersect at an angle of ${28}^{\circ }$ .

Answer to Problem 39CR

The sides of the parallelogram are 12.63 feet and 4.285 feet.

Explanation of Solution

Given information: The lengths of the diagonals of a parallelogram are 10 feet and 16

feet.

Calculation:

The below figure shows the given parallelogram.

  

In the above figure:

  $\begin{array}{l}{a}^2=5^2+8^2-2(5)(8)\cos ({180}^{\circ }-{28}^{\circ })=89-80\cos {152}^{\circ }\approx 159.6\Rightarrow a\approx 12.63\text{feet}.\\ b^2=5^2+8^2-2(5)(8)\cos {28}^{\circ }\approx 18.36\Rightarrow b\approx 4.285\text{feet}.\end{array}$