Answer:
21 ft
Step-by-step explanation:
Let's follow the given steps to find the length of the guy wire [tex]\sf AE [/tex].
Using the Pythagorean theorem to find the length of wire from the pole to the stake (AC):
[tex]\sf AC^2 = AB^2 + BC^2 [/tex]
[tex]\sf AC^2 = 4^2 + 5^2 [/tex]
[tex]\sf AC^2 = 16 + 25 [/tex]
[tex]\sf AC^2 = 41 [/tex]
[tex]\sf AC = \sqrt{41} [/tex]
So, the length of wire from the pole to the metal stake is [tex]\sf \sqrt{41} [/tex] feet.
Now, using similar triangles and the proportional property:
(The corresponding sides of a similar triangles are proportional.)
Using this:
[tex]\sf \dfrac{{AD}}{{AB}} = \dfrac{{AE}}{{AC}} [/tex]
[tex]\sf \dfrac{{9 \, \textsf{ft} + 4 \, \textsf{ft}}}{{4 \, \textsf{ft}}} = \dfrac{{x}}{{\sqrt{41}}} [/tex]
[tex]\sf \dfrac{{13 \, \textsf{ft}}}{{4 \, \textsf{ft}}} = \dfrac{{x}}{{\sqrt{41}}} [/tex]
[tex]\sf x = \dfrac{{13}}{{4}} \times \sqrt{41} [/tex]
[tex]\sf x \approx 20.810153771656 [/tex]
[tex]\sf x \approx 21 \textsf{ ft ( rounded to nearest foot)}[/tex]
So, the length of the guy wire, to the nearest foot, is 21 ft.
