Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

A box of chocolates shaped like a regular hexagon is placed snugly inside of a rectangular box as shown in the figure.If the side length of the hexagon is 4 inches, what are the dimensions of the rectangular box? (30°-60°-90° )

Sagot :

MrRoyal

A regular hexagon has 6 congruent sides.

The dimension of the rectangle is 8 inches by [tex]4\sqrt 3[/tex] inches

How to determine the length of the rectangle

Start by calculating the value of x using the following cosine ratio

[tex]\cos(60) = \frac{x}{4}[/tex]

Make x the subject

[tex]x = 4 * \cos(60)[/tex]

Evaluate cos(60)

[tex]x = 4 * 0.5[/tex]

[tex]x = 2[/tex]

So, the dimension of the rectangle is:

[tex]Length = 2x + 4[/tex]

[tex]Width = 2x\sqrt 3[/tex]

This gives

[tex]Length = 2 * 2 + 4[/tex]

[tex]Length = 8[/tex]

[tex]Width = 2 * 2\sqrt 3[/tex]

[tex]Width = 4\sqrt 3[/tex]

Hence, the dimension of the rectangle is 8 by [tex]4\sqrt 3[/tex]

Read more about hexagons at:

https://brainly.com/question/2264170

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.