Respuesta :

Answer:

x ≈ 28.2

Step-by-step explanation:

Using the sine rule then

[tex]\frac{sinx}{15}[/tex] = [tex]\frac{sin27}{11}[/tex] ( cross- multiply )

11sinx = 15sin27° ( divide both sides by 11 )

sin x = [tex]\frac{15sin27}{11}[/tex] ≈ 0.61907..

x = [tex]sin^{-1}[/tex](0.61907 ) ≈ 28.2

As suggested, we have to use the law of sines: it states that the ratio between a side and the sine of the opposite angle is constant in every triangle.

We know that one side length is 11, and the opposite angle is 27°

Another side length is 15, and the opposite angle is x.

So, the law of sines states that

[tex]\dfrac{11}{\sin(27)}=\dfrac{15}{\sin(x)}[/tex]

Solving for [tex]\sin(x)[/tex] we have

[tex]\sin(x) = \dfrac{15\sin(27)}{11}[/tex]

Which implies

[tex]x=\arcsin\left(\dfrac{15\sin(27)}{11}\right)[/tex]

Put this into a calculator to get

[tex]\arcsin\left(\dfrac{15\sin(27)}{11}\right)\approx 0.7[/tex]

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