Question

The accompanying diagram shows two cables ofequal length supporting a pole. Both cables are 14meters long, and they are anchored to points in theground that are 14 meters apart.14 mPole14 m14 mWhat is the exact height of the pole, in meters?Your answer

Answer 1

As shown in the figure:

The two cables and the ground like as an equilateral triangle

The length of each side = 14 m

The pole is perpendicular to the ground

So, there are two right angle triangle

From the left side triangle:

hypotenuse = 14 m

And the length from the cable to the pole = 14/2 = 7 m

Let the height of the pole = h

Using Pythagorean theorem:

$\begin{gathered} 14^2=7^2+h^2 \\ h^2=14^2-7^2=196-49 \\ h^2=147 \\ h=\sqrt[]{147}=\sqrt[]{3\cdot49}=7\sqrt[]{3} \end{gathered}$

So, the height of the pole = 7√3 meters.