Question

II. The following figure shows an infinite zigzag path with each zag
occurs at an angle of π/4. Find the total length of this infinite zigzag
path.
T/4
1
T/4/

I need help please, it would greatly appreciated!!

Answer 1

The length of the infinite zigzag path is 1

How to determine the length

Note that the infinite zigzag path is embedded in an isosceles triangle

Using angle π/4, we have that

Tan π/4 = opposite/ adjacent

$tan \frac{3. 412}{4} = \frac{x}{1}$

$tan 0. 7855 = x$

$x = 0. 014$

To find the longer part 'y',  use the Pythagorean theorem

$y^{2} = (0.014)^2 + (1)^2$

$y^2 = 1.879 * 10^-4 + 1$
$y^2 = 1. 00$

$y = \sqrt{1. 000}$

$y = 1. 000$

The length of the infinite zigzag path is the same as the length of the longer part of the triangle which equals 1.

Thus, the length of the infinite zigzag path is 1

Learn more about the Pythagorean theorem here:

https://brainly.in/question/48490459

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