Transmitter rope

A television transmitter 108 m high is anchored at 2/3 of its height (from the ground) by three ropes of equal length. How many meters of rope are needed for anchoring if it is embedded at a distance of 54 m from the foot of the mast, and we count 10% of the length of ropes for anchoring in addition?

Final Answer:

x =  297 m

Step-by-step explanation:

$$\begin{gathered} h=108\text{m} \\ {h}_1=\frac{2}{3}\cdot h=\frac{2}{3}\cdot 108=\frac{2\cdot 108}{3}=\frac{216}{3}=72\text{m} \\ n=3 \\ a=54\text{m} \\ {x}_1=\sqrt{a^2+h_1^2}=\sqrt{54^2+72^2}=90\text{m} \\ q=100\%+10\%=1+\frac{10}{100}=1.1 \\ x=n\cdot x_1\cdot q=3\cdot 90\cdot \frac{11}{10}=297\text{m} \end{gathered}$$

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