By trigonometric functions and law of cosines, the value of x associated with a missing angle in the geometric system is between 7.701 and 7.856.
How to find a missing variable associated to an angle by trigonometry
In this question we have a geometric system that includes a right triangle, whose missing angle is determined by the following trigonometric function:
sin (7 · x + 4) = 12/14
7 · x + 4 = sin⁻¹ (12/14)
7 · x + 4 ≈ 58.997°
7 · x = 54.997°
x ≈ 7.856
In addition, the geometric system also includes a obtuse-angle triangle and that angle can be also found by the law of the cosine:
7² = 8² + 6² - 2 · (8) · (6) · cos (7 · x + 4)
17/32 = cos (7 · x + 4)
7 · x + 4 = cos⁻¹ (17/32)
7 · x + 4 ≈ 57.910°
7 · x ≈ 53.910°
x ≈ 7.701
Hence, we conclude that the value of x associated with a missing angle in the geometric system is between 7.701 and 7.856.
To learn more on triangles: https://brainly.com/question/25813512
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