Chapter 8.5, Problem 27WE

a.

To determine

To calculate: $BD$.

Answer to Problem 27WE

  $BD=5\text{ units}$ .

Explanation of Solution

Given information: A rectangular box has length 4 units, width 3 units, and height 2 units.

  

Calculation:

BD is a diagonal of rectangle ABCDBD can be determined by the Pythagorean theorem, $BD=\sqrt{A{B}^2+B{C}^2}=\sqrt{4^2+3^2}=5\text{ units}$ .

b.

To determine

To calculate: $\angle GBD$.

Answer to Problem 27WE

  $\angle GBD=22°$ .

Explanation of Solution

Given information: A rectangular box has length 4 units, width 3 units, and height 2 units.

  

Calculation:

From the figure, $\tan \left(\angle GBD\right)=\frac{GD}{BD}=\frac{2}{5}$ ,

  $\Rightarrow {\text{ tan}}^{-1}\left(\tan \left(\angle GBD\right)\right)=\angle GBD={\tan }^{-1}\left(\frac{2}{5}\right)=21.80°\approx 22°$ .

Hence, $\angle GBD$ is of $22°$ .