Question

Jorge is setting up his tent. He is using two nylon ropes to pull the tent taut and stabilize it at each end. If the tent is 5 feet tall, and Jorge stakes the ropes into the ground 3 feet from the tent, what is the total length of nylon rope he will use, to the nearest tenth of a foot? Show all of your work.

Answer 1

Answer:

$5.8\:feet$

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.

$h^2=l_1^2+l_2^2$

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:

$h^2=5^2+3^2$

Evaluate the squares:

$h^2=25+9$

Add

$h^2=34$

Take square root:

$h=\sqrt{34}$

Use a scientific calculator

$h=5.83$

Round to the nearest tenth

$5.8 \:feet$