Chapter 6.4, Problem 11PPS

To determine

The length of CB.

Answer to Problem 11PPS

  $\text{BC = 6}\text{.3 feet}$

Explanation of Solution

Given:

The given figure is:

  $AB=6\text{ feet, AC = 2 feet and m}\angle \text{CAE = 65}\text{.}$

Calculation:

The opposite sides of rectangle are equal in length and there are 4 right angles.

The diagonals of a rectangle are perpendicular and bisect the angles at the vertex.

In the triangle CBD, diagonal is BC.

Using Pythagoras Theorem to find BC:

  $\begin{array}{l}{\left(BC\right)}^2={\left(CD\right)}^2+{\left(DB\right)}^2\\ {\left(BC\right)}^2={\left(6\right)}^2+{\left(2\right)}^2\\ {\left(BC\right)}^2=36+4\\ {\left(BC\right)}^2=40\\ BC=\sqrt{40}\\ BC\approx 6.3\text{ feet}\\ \text{BC = 6}\text{.3 feet}\end{array}$