Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 魅影直播 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 12: Q33. (page 480)

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

Short Answer

Expert verified

The volume of box is $336.1 {鈥夆赌塽苍颈迟}^{3}$ .

Step by step solution

Step 1. Given information.

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

The figure provided in the question,

Step 2. Determine the height.

Use Pythagoras theorem,

$\begin{matrix} \sqrt{{(8)}^{2} + {(6)}^{2}} = d \\ d = \sqrt{64 + 36} [square] \\ d = 10 [simplify] \end{matrix}$

Now, the height of the prism is,

$\begin{matrix} \tan 35^{鈭�} = \frac{h}{10} \\ h = 10 \tan 35^{鈭�} [crossmultiply] \end{matrix}$

Step 3. Determine the total volume.

The volume of the box is:

$\begin{matrix} v = 8 脳 6 脳 10 \tan 35^{鈭�} \\ = 336.1 [simplify] \end{matrix}$

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魅影直播

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the height.

Step 3. Determine the total volume.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

魅影直播

A diagonal of a box forms a35鈭�angle with a diagonal of the base. Use trigonometry to approximate the volume of the box.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the height.

Step 3. Determine the total volume.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Calculus

Decision Maths

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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