The mast

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

Correct result:

x =  11.481 m

Solution:

l=40 m l2=l/2=40/2=20 m r=252l22=252202=15 m n=8 A=360/n/2=360/8/2=452=22.5  sinA=(x/2)/r x=2 r sin(A rad)=2 r sin(A π180 )=2 15 sin(22.5 3.1415926180 )=11.481 ml=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=\dfrac{ 45 }{ 2 }=22.5 \ ^\circ \ \\ \sin A=(x/2) / r \ \\ x=2 \cdot \ r \cdot \ \sin( A ^\circ \rightarrow\ \text{rad} )=2 \cdot \ r \cdot \ \sin( A ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=2 \cdot \ 15 \cdot \ \sin( 22.5 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=11.481 \ \text{m}



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