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 answer:

x =  25.6125 m
A =  38.6598 °

Step-by-step explanation:

$$\begin{gathered} l=20\text{ m } \\ h=8\text{ m } \\ a=l\mathrm{/}2=20\mathrm{/}2=10\text{ m } \\ {c}^2=a^2+h^2 \\ c=\sqrt{a^2+h^2}=\sqrt{10^2+8^2}=2\sqrt{41}\text{ m}\doteq 12.8062\text{ m } \\ x=2\cdot c=2\cdot 12.8062=4\sqrt{41}=25.6125\text{ m} \end{gathered}$$

$$\begin{gathered} \sin A=h:c \\ {A}_1=\arcsin (h\mathrm{/}c)=\arcsin (8\mathrm{/}12.8062)\doteq 0.6747\text{ rad } \\ A=A_1{\to }^{\circ }=A_1\cdot {{\displaystyle \frac{180}{\pi }}}^{\circ }=0.6747\cdot {{\displaystyle \frac{180}{\pi }}}^{\circ }=38.66^{\circ }=38.6598^{\circ }=38^{\circ }39^{\mathrm{\prime }}35\mathrm{"} \end{gathered}$$

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