The arc length is 0.785 units and the diagonal is √2 units
How to determine the lengths?
The question requires that we determine the lengths of the blue line and the arc
The blue line is the diagonal of the square, whose side length (l) is
l = 1
The diagonal is then calculated as:
[tex]d = l * \sqrt 2[/tex]
This gives
[tex]d = 1 * \sqrt 2[/tex]
[tex]d = \sqrt 2[/tex]
The diagonal divides the vertex of the square into 45 degrees a piece, and the diagonal represents the radius of the arc
This means that:
[tex]r = \sqrt 2[/tex]
[tex]\theta = 45^o[/tex]
The arc length is:
[tex]l = \frac{\theta}{360} * \pi r^2[/tex]
So, we have:
[tex]l = \frac{45^o}{360} * 3.14 * \sqrt 2^2[/tex]
This gives
[tex]l = \frac{282.6}{360}[/tex]
Divide
l = 0.785
Hence, the arc length is 0.785 units and the diagonal is √2 units
Read more about arc lengths at:
https://brainly.com/question/2005046
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