Respuesta :
To solve the problem we must know about Sine Rule.
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.
The value of w is 4.0 cm.
Given to us
- VW = 3.3 cm,
- ∠U = 31°,
- ∠W = 39°,
Using the sine law,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]
Substitute the values,
[tex]\dfrac{Sin\ W}{w} = \dfrac{Sin\ U}{VW}[/tex]
[tex]\dfrac{Sin\ 39^o}{w}=\dfrac{Sin\ 31^o}{3.3}[/tex]
[tex]w=\dfrac{(Sin\ 39^o) \times 3.3}{Sin\ 31^o}[/tex]
w = 4.03224 cm ≈ 4.0 cm
Hence, the value of w is 4.0 cm.
Learn more about Sine Rule:
https://brainly.com/question/17289163
