Respuesta :

tdpuppies14
Since the triangle above is a right triangle, we can use trigonometry to solve for x. In this case, the ratio SOH or Sin. x = opposite/ hypotenuse. We can substitute the variables with the side lengths shown.

Sin. x = 66/79
Sin. x = 0.83544303797
Using a trigonometric table we can look down the sin. column to see which number is closest to 0.83544303797. In this case the closest degree is 48.

Final Answer: x = 48

Answer:

The value of x is 56.7 mm.

Step-by-step explanation:

In a right angled triangle

[tex]\sin\theta=\frac{Perpendicular}{Hypotenuse}=\frac{Opposite}{Hypotenuse}[/tex]

The given triangle is a right angled triangle with opposite sides 66 mm and hypotenuse 79mm.

[tex]\sin x=\frac{66}{79}[/tex]

Taking sin⁻¹ on both the sides.

[tex]\sin^{-1}(\sin x^{\circ})=\sin^{-1}(\frac{66}{79})[/tex]

[tex]x^{\circ}=\sin^{-1}\frac{66}{79}[/tex]

[tex]x^{\circ}=56.66^{\circ}[/tex]

[tex]x\approx 56.7[/tex]

Therefore the value of x is 56.7 mm.