Question

a flying squirrels nest is 12 feet high in a tree. from its nest, the flying squirrel glides 13 feet to reach an acorn that is on the ground. how far is the acorn from the base of the tree? feet

Explanation:

Step1: Identify the problem as a right - triangle problem

We can consider a right - triangle where the height of the nest is one leg ($a = 12$ feet), the distance from the base of the tree to the acorn is the other leg (let's call it $b$), and the gliding distance of the squirrel is the hypotenuse ($c = 13$ feet). According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$.

Step2: Rearrange the Pythagorean theorem to solve for $b$

We get $b=\sqrt{c^{2}-a^{2}}$. Substitute $a = 12$ and $c = 13$ into the formula: $b=\sqrt{13^{2}-12^{2}}=\sqrt{(13 + 12)(13 - 12)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$).

Step3: Calculate the value of $b$

$b=\sqrt{(13 + 12)(13 - 12)}=\sqrt{25\times1}=\sqrt{25}=5$.

Answer:

5