Answer:
Value of x is 13.47
Answer is given below with explanations.
Step-by-step explanation:
[tex]in \: first \: triangle \\ sin( \alpha ) = \frac{opposite \: side}{hypotenuse} \\ here \: \alpha = 60 \: degrees \\ hypotenuse = 11 \\ then \: \sin(60) = \frac{opposite \: side}{11} \\ \frac{ \sqrt{3} }{2} = \frac{opposite \: side}{11} \\ opposite \: side = \frac{11 \sqrt{3} }{2} \\ let \: y = \frac{11 \sqrt{3} }{2} \\ in \: second \: triangle \\ \sin( \alpha ) = \frac{opposite \: side}{hypotenuse} \\ here \: \alpha = 45 \: degrees \\ \sin(45) = \frac{y}{x} \\ \frac{1}{ \sqrt{2} } = \frac{y}{x} \\ x = y \sqrt{2} \\ x = ( \frac{11 \sqrt{3} }{2} ) \sqrt{2} \\ x = \frac{11 \sqrt{3} }{ \sqrt{2} } \\ x = 13.472 \\ then \: x \: is \: approximately \: equal \: to \: 13.47[/tex]
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