Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To find the diameter of the circular window, we can use the information provided. Here is a detailed, step-by-step solution:
1. Understanding the Problem:
- We have a circular window with an [tex]$8$[/tex]-foot horizontal shelf.
- There is a [tex]$2$[/tex]-foot vertical brace that bisects the horizontal shelf and passes through the center of the window.
2. Recognize the Geometry:
- The horizontal shelf runs across the diameter of the circular window.
- The vertical brace runs perpendicular to the shelf and also intersects the center of the circle.
3. Divide and Conquer:
- By dividing the horizontal shelf into two equal parts, we create two right triangles. Each part of the shelf will be [tex]$4$[/tex] feet (since [tex]$8$[/tex] feet divided by [tex]$2$[/tex] is [tex]$4$[/tex] feet).
4. Identify the Elements of the Right Triangle:
- The base of the right triangle is [tex]$4$[/tex] feet (half of the shelf).
- The height of the right triangle is [tex]$2$[/tex] feet (the brace).
5. Use the Pythagorean Theorem:
- The radius of the circular window is the hypotenuse of the right triangle formed by the base (half of the shelf) and the height (the brace).
- The Pythagorean theorem states that in a right triangle, [tex]\( a^2 + b^2 = c^2 \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the lengths of the legs, and [tex]\( c \)[/tex] is the length of the hypotenuse (the radius in our case).
6. Calculate the Radius:
- Let's denote the radius by [tex]\( r \)[/tex].
- According to the Pythagorean theorem:
[tex]\[ r^2 = 4^2 + 2^2 \][/tex]
[tex]\[ r^2 = 16 + 4 \][/tex]
[tex]\[ r^2 = 20 \][/tex]
[tex]\[ r = \sqrt{20} = \sqrt{4 \times 5} = 2 \sqrt{5} \approx 4.47213595499958 \][/tex]
7. Determine the Diameter:
- The diameter of the circle is twice the radius.
- Hence, the diameter [tex]\( D \)[/tex] is given by:
[tex]\[ D = 2 \times r = 2 \times 4.47213595499958 \approx 8.94427190999916 \][/tex]
Therefore, the diameter of the window is approximately [tex]\( 8.944 \)[/tex] feet.
Diamond = 8.944 feet
1. Understanding the Problem:
- We have a circular window with an [tex]$8$[/tex]-foot horizontal shelf.
- There is a [tex]$2$[/tex]-foot vertical brace that bisects the horizontal shelf and passes through the center of the window.
2. Recognize the Geometry:
- The horizontal shelf runs across the diameter of the circular window.
- The vertical brace runs perpendicular to the shelf and also intersects the center of the circle.
3. Divide and Conquer:
- By dividing the horizontal shelf into two equal parts, we create two right triangles. Each part of the shelf will be [tex]$4$[/tex] feet (since [tex]$8$[/tex] feet divided by [tex]$2$[/tex] is [tex]$4$[/tex] feet).
4. Identify the Elements of the Right Triangle:
- The base of the right triangle is [tex]$4$[/tex] feet (half of the shelf).
- The height of the right triangle is [tex]$2$[/tex] feet (the brace).
5. Use the Pythagorean Theorem:
- The radius of the circular window is the hypotenuse of the right triangle formed by the base (half of the shelf) and the height (the brace).
- The Pythagorean theorem states that in a right triangle, [tex]\( a^2 + b^2 = c^2 \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the lengths of the legs, and [tex]\( c \)[/tex] is the length of the hypotenuse (the radius in our case).
6. Calculate the Radius:
- Let's denote the radius by [tex]\( r \)[/tex].
- According to the Pythagorean theorem:
[tex]\[ r^2 = 4^2 + 2^2 \][/tex]
[tex]\[ r^2 = 16 + 4 \][/tex]
[tex]\[ r^2 = 20 \][/tex]
[tex]\[ r = \sqrt{20} = \sqrt{4 \times 5} = 2 \sqrt{5} \approx 4.47213595499958 \][/tex]
7. Determine the Diameter:
- The diameter of the circle is twice the radius.
- Hence, the diameter [tex]\( D \)[/tex] is given by:
[tex]\[ D = 2 \times r = 2 \times 4.47213595499958 \approx 8.94427190999916 \][/tex]
Therefore, the diameter of the window is approximately [tex]\( 8.944 \)[/tex] feet.
Diamond = 8.944 feet
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
