Antenna mast

The antenna mast is 26 meters high. It is fixed by four steel cables suspended 1.6 meters below the highest point of the mast and anchored to the ground at the vertices of a square with a side length of 14 meters. The mast is erected in the center of this square. Calculate the total length of the ropes if 1.5 m is added to secure each one.

Correct answer:

x =  111.3269 m

Step-by-step explanation:

$$\begin{gathered} h=26\text{m} \\ {h}_2=h-1.6=26-1.6=\frac{122}{5}=24.4\text{m} \\ a=14\text{m} \\ u=\sqrt{2}\cdot a=\sqrt{2}\cdot 14=14\sqrt{2}\text{m}\doteq 19.799\text{m} \\ {x}_1=\sqrt{h_2^2+(u/2{)}^2}=\sqrt{24.4^2+(19.799/2{)}^2}\doteq 26.3317\text{m} \\ x=4\cdot (x_1+1.5)=4\cdot (26.3317+1.5)=111.3269\text{m} \end{gathered}$$

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