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Q33.

Expert-verified
Found in: Page 480

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

# A diagonal of a box forms a ${35}^{\circ }$ angle with a diagonal of the base. Use trigonometry to approximate the volume of the box.

The volume of box is$336.1{\text{\hspace{0.17em}\hspace{0.17em}unit}}^{3}$ .

See the step by step solution

## Step 1. Given information.

A diagonal of a box forms${35}^{\circ }$ angle with a diagonal of the base.

The figure provided in the question,

## Step 2. Determine the height.

Use Pythagoras theorem,

$\begin{array}{c}\sqrt{{\left(8\right)}^{2}+{\left(6\right)}^{2}}=d\\ d=\sqrt{64+36}\text{[square]}\\ d=10\text{[simplify]}\end{array}$

Now, the height of the prism is,

$\begin{array}{c}\mathrm{tan}{35}^{\circ }=\frac{h}{10}\\ h=10\mathrm{tan}{35}^{\circ }\text{[cross multiply]}\end{array}$

## Step 3. Determine the total volume.

The volume of the box is:

$\begin{array}{c}v=8×6×10\mathrm{tan}{35}^{\circ }\\ =336.1\text{[simplify]}\end{array}$