Respuesta :
The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The length of the side j is 30.6 cm.
What is Sine rule?
The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
Given the length of i is 53 cm, while the measure of the ∠I is 120°. Also, the measure of ∠J is 30°. Therefore, the length of the side j is,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}\\\\\dfrac{Sin\ I}{i} =\dfrac{Sin\ J}{j} \\\\\dfrac{Sin\ 120^o}{53} =\dfrac{Sin\ 30^o}{j} \\\\j = \dfrac{Sin\ 30^o \times 53}{Sin\ 120^o}\\\\j = 30.5995 \approx 30.6\rm\ cm[/tex]
Hence, the length of the side j is 30.6 cm.
Learn more about Sine Rule:
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