Question

4 a guy wire is attached to an upright pole 6 meters above the ground. if the wire is anchored to the ground 4 meters from the base of the pole, how long is the wire?

Explanation:

Step1: Identify the triangle type

The pole, ground, and guy wire form a right - triangle, where the height of the pole (6 meters) and the distance from the base of the pole to the anchor (4 meters) are the two legs of the right - triangle, and the guy wire is the hypotenuse. We can use the Pythagorean theorem, which states that for a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 6\) meters and \(b = 4\) meters.

Step2: Apply the Pythagorean theorem

Substitute \(a = 6\) and \(b = 4\) into the Pythagorean theorem formula. So we have \(c^{2}=6^{2}+4^{2}\). Calculate \(6^{2}=36\) and \(4^{2}=16\). Then \(c^{2}=36 + 16=52\).

Step3: Find the length of the hypotenuse

To find \(c\), we take the square root of both sides. \(c=\sqrt{52}\). Simplify \(\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}\approx2\times3.606 = 7.21\) meters (or we can leave it in the form \(2\sqrt{13}\) meters, but a decimal approximation is also acceptable).

Answer:

The length of the wire is \(2\sqrt{13}\) meters (or approximately \(7.21\) meters).