Chapter 8.5, Problem 22WE

To determine

To find: the angle of rhombus.

Answer to Problem 22WE

The angles of rhombus are $136.4°$ and $43.6°$ .

Explanation of Solution

Given:

The diagonals of rhombus are 4 and 10.

Calculation:

Diagonals of the rhombus are perpendicular bisector. Diagonals of the rhombus bisect the angle of rhombus as well.

Hence, the rhombus is shown below:

In triangle AOD,

  $\begin{array}{c}\tan \angle OAD=\frac{\text{Height}}{\text{Base}}\\ \tan \angle OAD=\frac{\text{5}}{\text{2}}\\ \angle OAD\approx 68.2°\end{array}$

Angle BAD is,

  $\begin{array}{c}\angle BAD=2\angle OAD\\ \angle BAD=2\left(68.2°\right)\\ =136.4°\end{array}$

Similarly,

In triangle AOD,

  $\begin{array}{c}\tan \angle ADO=\frac{\text{Height}}{\text{Base}}\\ \tan \angle ADO=\frac{2}{5}\\ \angle ADO\approx 21.8°\end{array}$

Angle ADC is,

  $\begin{array}{c}\angle ADC=2\angle ADO\\ \angle BAD=2\left(21.8°\right)\\ =43.6°\end{array}$

Thus, the angles of rhombus are

$136.4°$ and $43.6°$ .