Chapter 9.10, Problem 12PSB

To determine

To find:The length of each of the diagonals

Answer to Problem 12PSB

The length of the diagonals are $5.6\text{ in}$ and $11.0\text{ in}$

Explanation of Solution

Given information:The following information has been given

Each side of the rhombus is $6.2\text{ in}$

One diagonal of the rhombus makes angle ${27}^0$

Formula used:Basic trigonometric definitions have been used

Calculation:Now, we know that the diagonals of a rhombus are perpendicular to each other. We assume the diagonals to be of lengths $2x$ and $2y$ each.

Hence, in a quarter triangle of the rhombus, we can say that

  $\sin {27}^0=\frac{x}{6.2\text{ in}}$ , and

  $\cos {27}^0=\frac{y}{6.2\text{ in}}$

Thus, from these two equations, we get

  $2x=5.63\text{ in}$ , and

  $2y=11.05\text{ in}$