A hummingbird lives in a nest that is 8 meters high in a tree. The hummingbird flies straight from its nest to a flower on the ground, a distance of 9 meters. How far is the flower from the base of the tree? If necessary, round to the nearest tenth.

We have been given that a hummingbird lives in a nest that is 8 meters high in a tree. The hummingbird flies straight from its nest to a flower on the ground, a distance of 9 meters. We are asked to find the distance between flower and the base of tree.

We will draw a right triangle to represent the given scenario as shown in the attached file.

We will use Pythagoras theorem to find the distance between flower and the base of tree as:

[tex]x^2+8^2=9^2[/tex]

[tex]x^2+64=91[/tex]

[tex]x^2+64-64=91-64[/tex]

[tex]x^2=27[/tex]

Now, we will take positive square root of both sides as:

[tex]\sqrt{x^2}=\sqrt{27}[/tex]

[tex]x=5.1961524227066319[/tex]

Upon rounding to nearest tenth, we will get:

[tex]x\approx 5.2[/tex]

Therefore, the flower is approximately 5.2 meters away from the base of the tree.