Question

warm-up
a camper ties a rope from a tree to the ground to help build a shelter. the rope is 8 feet long, and it is tied 6 feet up the tree. how far from the tree is the rope anchored to the ground? use the pythagorean theorem to find the answer.
tree
6 feet
8 feet
ground
type the correct answer in the box. use numerals instead of words. express your answer as a decimal number rounded to the nearest tenth.
the rope is anchored feet from the tree.

Explanation:

Step1: Identify the sides of the right triangle

The tree, ground, and rope form a right triangle. The rope is the hypotenuse ($c = 8$ feet), the height on the tree is one leg ($a = 6$ feet), and the distance from the tree to the anchor is the other leg ($b$), which we need to find. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$.

Step2: Rearrange the formula to solve for $b$

We can rearrange the formula to $b=\sqrt{c^{2}-a^{2}}$. Substitute $a = 6$ and $c = 8$ into the formula: $b=\sqrt{8^{2}-6^{2}}=\sqrt{64 - 36}=\sqrt{28}$.

Step3: Calculate the square root and round

$\sqrt{28}\approx5.3$ (rounded to the nearest tenth).

Answer:

5.3