Antenna mast

An antenna mast is 26 metres high. It is secured by four steel cables attached 1.6 metres below the highest point of the mast and anchored to the ground at the vertices of a square with a side length of 14 metres. The mast stands at the centre of this square. Calculate the total length of cable needed if 1.5 m is added to each cable for securing.

Final 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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