Answer:
[tex]5.8\:feet[/tex]
Step-by-step explanation:
The total length of the nylon rope, the height of the tent, the ground distance from the stake to the tent, forms a right angle triangle.
We can apply the Pythagoras Theorem to find the total length of nylon rope Jorge will use.
According to the Pythagoras Theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.
[tex]h^2=l_1^2+l_2^2[/tex]
Note that the height of the tent and the ground distance to the stake formed the legs, while the length of the nylon rope forms the hypotenuse.
This implies that:
[tex]h^2=5^2+3^2[/tex]
Evaluate the squares:
[tex]h^2=25+9[/tex]
Add
[tex]h^2=34[/tex]
Take square root:
[tex]h=\sqrt{34}[/tex]
Use a scientific calculator
[tex]h=5.83[/tex]
Round to the nearest tenth
[tex]5.8 \:feet[/tex]
By modeling the tent with two right triangles, we will see that the length of the rope must be 11.66 ft.
The total length of the rope needed will be equal to twice the hypotenuse of a right triangle with cathetus of 5ft and 3ft, remember that by the Pythagorean theorem the square of the hypotenuse is equal to the sum of the squares of the cathetus, then:
H^2 = (5ft)^2 + (3ft)^2
H = √( (5ft)^2 + (3ft)^2) = 5.83ft
Then the length of the rope is:
L = 2*H = 2*5.83ft = 11.66 ft.
If you want to learn more about right triangles, you can read:
https://brainly.com/question/2217700
