Chapter 12.6, Problem 14WE

To determine

To determine the length of diagonals.

Answer to Problem 14WE

Length of diagonal AC is 7.83

Length of diagonal BD is 11.16

Explanation of Solution

Given information :

Two sides of parallelogam are 6cm and 8 cm

Given angle is ${65}^{\circ }$

We know that the adjacent angles of parallelogram are supplementary.

Hence,

  

Use cosine law to determine the length.

Cosine formula states that,

  $\cos A=\frac{b^2+c^2-a^2}{2bc}$

Putting values we get,

  $\begin{array}{l}\cos {65}^{\circ }=\frac{6^2+8^2-{\left(AC\right)}^2}{2\left(6\right)\left(8\right)}\\ 40.57=84-{\left(AC\right)}^2\\ A{C}^2=43.43\\ AC=6.6\end{array}$

Hence length of diagonal AC is 7.83

Similarly,

  $\begin{array}{l}\cos {115}^{\circ }=\frac{6^2+8^2-{\left(BD\right)}^2}{2\left(6\right)\left(8\right)}\\ -40.57=84-{\left(BD\right)}^2\\ B{D}^2=124.57\\ BD=11.16\end{array}$

Length of diagonal BD is 11.16