Chapter 8.5, Problem 23WE

To determine

To find: the length of longer diagonal of rhombus.

Answer to Problem 23WE

The length of longer diagonal of rhombus is $174.24\text{cm}$ .

Explanation of Solution

Given:

The shorter diagonal of rhombus with angle $70°$ is 122 cm long.

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 AOB,

  $\begin{array}{c}\tan \angle OAB=\frac{\text{Height}}{\text{Base}}\\ \tan 35°=\frac{61}{AO}\\ AO\approx 87.12\text{cm}\end{array}$

Thus, the length of other diagonal AC is calculated as follows:

  $\begin{array}{c}AC=2AO\\ =2\left(87.12\text{cm}\right)\\ =174.24\text{cm}\end{array}$

Thus, the length of longer diagonal of rhombus is $174.24\text{cm}$ .