Question

how long is the wire that supports the tree? 10 5.6 ft 3.3 ft

Explanation:

Step1: Identify the right - triangle

The situation forms a right - triangle with legs of lengths \(a = 5.6\) ft and \(b=3.3\) ft, and the wire length \(c\) is the hypotenuse.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), so \(c^{2}=(5.6)^{2}+(3.3)^{2}\).
First, calculate \((5.6)^{2}=5.6\times5.6 = 31.36\) and \((3.3)^{2}=3.3\times3.3 = 10.89\).
Then \(c^{2}=31.36 + 10.89=42.25\).

Step3: Solve for \(c\)

Take the square - root of both sides: \(c=\sqrt{42.25}\). Since \(\sqrt{42.25}=6.5\), the length of the wire is \(6.5\) ft.

Answer:

\(6.5\) ft