By <em>trigonometric</em> functions and law of cosines, the value of x associated with a <em>missing</em> angle in the <em>geometric</em> system is between 7.701 and 7.856.
<h3>How to find a missing variable associated to an angle by trigonometry</h3>
In this question we have a <em>geometric</em> system that includes a <em>right</em> triangle, whose missing angle is determined by the following <em>trigonometric</em> 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 <em>geometric</em> system also includes a <em>obtuse-angle</em> 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 <em>missing</em> angle in the <em>geometric</em> system is between 7.701 and 7.856.
To learn more on triangles: brainly.com/question/25813512
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Answer:
Length of the side opposite to angle 
is 31.49
Step-by-step explanation:
Included angle can be defined as the angle in between two sides of the triangle.
So angle is in between sides 16 and 21.
Refer to the attachment for triangle diagram.
To find the length of opposite side, use cosine rule as follows
From the diagram, 
Substituting the values in the formula,
Simplifying,
Taking square root on both sides,
Therefore length of third side is 31.49
Answer:
A. 1,485 cubic cm. B. 27
Step-by-step explanation:
The new prism is dilated by a factor of 3, that means it's made bigger, 3 times bigger on each side.
The dimensions of the new prism are then 12 cm by 7.5 cm by 16.5 cm.
Its volume is then of 12 x 7.5 x 16.5 = 1,485 cubic cm
To answer the second question...
Let's calculate the volume of the original prism:
The original prism's volume was 4 x 2.5 x 5.5 = 55 cubic cm
The new volume is then 1485 / 55 = 27 times bigger than the original.
Which is normal, since we increased each side (dimension) by a factor of 3, so 3x3x3 = 27.
It’s the first option, 5 + c
