Question

a flying squirrels nest is 6 meters high in a tree. from its nest, the flying squirrel glides 9 meters to reach an acorn that is on the ground. how far is the acorn from the base of the tree? if necessary, round to the nearest tenth. meters

Explanation:

Step1: Identify the right - angled triangle

The height of the nest in the tree is one leg ($a = 6$ meters) of a right - angled triangle, the gliding distance is the hypotenuse ($c = 9$ 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 $a = 6$ and $c = 9$ into the formula: $b=\sqrt{9^{2}-6^{2}}=\sqrt{81 - 36}=\sqrt{45}$.

Step3: Calculate and round

$\sqrt{45}\approx6.7$ (rounded to the nearest tenth).

Answer:

$6.7$