Sailboat

The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck.

Correct result:

x =  25.612 m
A =  38.66 °

Solution:

$l=20 \ \text{m} \ \\ h=8 \ \text{m} \ \\ a=l/2=20/2=10 \ \text{m} \ \\ \ \\ c^2=a^2+h^2 \ \\ c=\sqrt{ a^2+h^2 }=\sqrt{ 10^2+8^2 } \doteq 2 \ \sqrt{ 41 } \ \text{m} \doteq 12.8062 \ \text{m} \ \\ \ \\ x=2 \cdot \ c=2 \cdot \ 12.8062=4 \ \sqrt{ 41 }=25.612 \ \text{m}$

$\sin A=h : c \ \\ A_{1}=\arcsin(h/c)=\arcsin(8/12.8062) \doteq 0.6747 \ \text{rad} \ \\ \ \\ A=A_{1} \rightarrow \ ^\circ =A_{1} \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =0.674740942221 \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =38.66 \ \ ^\circ =38.66 ^\circ =38^\circ 39'35"$

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