Question

Como se hace y la respuesta

Answer 1

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:

$d = l * \sqrt 2$

This gives

$d = 1 * \sqrt 2$

$d = \sqrt 2$

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:

$r = \sqrt 2$

$\theta = 45^o$

The arc length is:

$l = \frac{\theta}{360} * \pi r^2$

So, we have:

$l = \frac{45^o}{360} * 3.14 * \sqrt 2^2$

This gives

$l = \frac{282.6}{360}$

Divide

l = 0.785

Hence, the arc length is 0.785 units and the diagonal  is √2 units

Read more about arc lengths at:

brainly.com/question/2005046

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