Question

an oak tree is 6 meters tall and a bird is standing on the ground 4 meters from the tree. if the bird flies directly to the top of the tree, how far will it fly? if necessary, round to the nearest tenth. meters

Explanation:

Step1: Identify right - triangle sides

The height of the tree is one leg ($a = 6$ meters) and the distance from the tree to the bird on the ground is the other leg ($b = 4$ meters) of a right - triangle. The path of the bird's flight is the hypotenuse $c$.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$. Substitute $a = 6$ and $b = 4$ into the formula: $c=\sqrt{6^{2}+4^{2}}=\sqrt{36 + 16}=\sqrt{52}$.

Step3: Calculate and round

$\sqrt{52}\approx7.2$ (rounded to the nearest tenth).

Answer:

$7.2$