Answer:
12.2 feet
Step-by-step explanation:
The key to this problem is trigonometry.
Imagine a right triangle. With a height, 10 ft (representing the tree's height), and a base of 7 ft (representing the horizontal distance to the worm).
Now the hypoteneuse length, or otherwise the distance from the worm is unknown.
So this is where we can use the pythagorean theorem.
[tex]a^2 + b^2 = c^2[/tex]
[tex]c[/tex] here is the hypoteneuse length, and [tex]a[/tex] and [tex]b[/tex] are the other lengths of the triangle.
Since we know a and b we can solve for c.
But first we will square root both sides of the equation to get [tex]c[/tex] and not [tex]c^2[/tex].
[tex]\sqrt{a^2 + b^2} = c[/tex]
Now just plug in our values for a and b respectively. (It doesn't matter what number replaces a or b, just make sure you are replacing a and b with the 2 known values) Calculate.
[tex]\sqrt{10^2 + 7^2} = \sqrt{100 + 49} = \sqrt{149} = 12.206....[/tex]
Round to the nearest tenth.
[tex]12.2[/tex] feet
