Question

a hummingbird lives in a nest that is 36 feet high in a tree. the hummingbird flies 45 feet to get from its nest to a flower on the ground. how far is the flower from the base of the tree? feet

Explanation:

Step1: Apply the Pythagorean theorem

Let the height of the nest be \(a = 36\) feet, the distance the humming - bird flies be \(c=45\) feet, and the distance from the base of the tree to the flower be \(b\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), so \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute the values of \(a\) and \(c\)

Substitute \(a = 36\) and \(c = 45\) into the formula \(b^{2}=c^{2}-a^{2}\). Then \(b^{2}=45^{2}-36^{2}\).
We know that \(45^{2}=45\times45 = 2025\) and \(36^{2}=36\times36=1296\). So \(b^{2}=2025 - 1296\).

Step3: Calculate \(b^{2}\) and then \(b\)

\(b^{2}=2025-1296 = 729\). Since \(b>0\) (distance cannot be negative), and \(b=\sqrt{729}\).
Because \(27\times27 = 729\), so \(b = 27\).

Answer:

27