The mast

A 40 m high mast is secured in half by eight ropes 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.

Final Answer:

x =  11.4805 m

Step-by-step explanation:

$$\begin{gathered} l=40\text{m} \\ {l}_2=l/2=40/2=20\text{m} \\ r=\sqrt{25^2-l_2^2}=\sqrt{25^2-20^2}=15\text{m} \\ n=8 \\ A=360/n/2=360/8/2=\frac{45}{2}=22.5{}^{\circ } \\ \sin A=(x/2)/r \\ x=2\cdot r\cdot \sin (A°\to \text{rad})=2\cdot r\cdot \sin (A°\cdot \frac{\pi }{180})=2\cdot 15\cdot \sin (22.5°\cdot \frac{3.1415926}{180})=11.481=11.4805\text{m} \end{gathered}$$

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