Let's begin with recalling the Pythagorean Theorem.
In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
a^2+ b^2= c^2
Now, we are given that Blake is sitting up his tent, which is 8 ft tall, and that the tether can be staked no more than 2 ft from the tent. Let's make a simplified diagram describing this situation. We will call the length of the tether x.
As we can see, the tether and the side of the tent form a right triangle with the ground. Therefore, we can use the Pythagorean Theorem to evaluate the length of the tether.
8^2+2^2=x^2
Let's solve the above equation. Notice that, since x represents the length, we will consider only the positive case when taking a square root of x^2.
