Question

a flying squirrels nest is 12 meters high in a tree. from its nest, the flying squirrel glides 20 meters to reach an acorn that is on the ground. how far is the acorn from the base of the tree? meters

Explanation:

Step1: Identify the right - angled triangle

The height of the nest in the tree is one leg ($a = 12$ meters), the gliding distance is the hypotenuse ($c = 20$ meters), and we need to find the other leg ($b$).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We can rewrite it to solve for $b$: $b=\sqrt{c^{2}-a^{2}}$.
Substitute $a = 12$ and $c = 20$ into the formula: $b=\sqrt{20^{2}-12^{2}}=\sqrt{(20 + 12)(20 - 12)}=\sqrt{32\times8}=\sqrt{256}$.

Step3: Calculate the value of $b$

$\sqrt{256}=16$.

Answer:

16