Question

2 fill in the blank 1 point a bird flies down 10 meters directly to the floor, now the bird is 6 meters from the bottom of the tree. how tall is the tree? type your answer... meters

Explanation:

Step1: Identify the triangle type

This is a right - triangle problem, where the hypotenuse (the distance the bird flew) is 10 meters, one leg (distance from the bottom of the tree) is 6 meters, and the other leg is the height of the tree (let's call it \(h\)). We can use the Pythagorean theorem, which states that for a right - triangle with legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). In this case, we want to find \(a\) (the height of the tree), so we can re - arrange the formula to \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute the values into the formula

We know that \(c = 10\) meters and \(b=6\) meters. Substitute these values into the formula:
\(h=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}\)

Step3: Calculate the square root

\(\sqrt{64}=8\)

Answer:

8