In the figure below, $a = 8 , b = 12$, and $c = 13$. Use this information to solve the parallelogram for $\theta$. The diagonals of the parallelogram are represented by $c$ and $d$. Round answer to two decimal places.

A) 101.72°
B) 95.86
C) 90.00°
D) 91.46
E) 78.28°

Question

In the figure below, $a = 8 , b = 12$, and $c = 13$. Use this information to solve the parallelogram for $\theta$. The diagonals of the parallelogram are represented by $c$ and $d$. Round answer to two decimal places.

A) 101.72° 
B) 95.86 
C) 90.00° 
D) 91.46 
E) 78.28°

Quizplus · Accepted Answer

We know that the diagonals of a parallelogram bisect each other. Therefore, we can find half the diagonal by dividing c by 2: $\frac{c}{2} = \frac{13}{2} = 6.5$. Using this value as the opposite side and 8 as the adjacent side, we can find the value of $\theta$ using the inverse tangent function: $\theta = \tan^{-1}\left(\frac{6.5}{8}\right) \approx \boxed{101.72^\circ}$ (rounded to two decimal places).

In the Figure Below a=8,b=12a = 8 , b = 12a=8,b=12

In the Figure Below $a = 8 , b = 12$