Answer :
Angle x is [tex]\( 94.1^\circ \)[/tex]. The correct option C.
To solve for x in the triangle using the cosine rule,
Given:
BC = 11
AB = 8
AC = 7
We need to find x.
Cosine Rule Application:
The cosine rule states:
[tex]\[ BC^2 = AB^2 + AC^2 - 2 \cdot AB \cdot AC \cdot \cos(x) \][/tex]
Substitute the given values:
[tex]\[ 11^2 = 8^2 + 7^2 - 2 \cdot 8 \cdot 7 \cdot \cos(x) \][/tex]
Calculate each term:
121 = 64 + 49 - 112 cos(x)
Combine like terms:
121 = 113 - 112 cos(x)
Subtract 113 from both sides:
8 = -112 cos(x)
Divide both sides by -112:
[tex]\[ \cos(x) = \frac{8}{-112} \]\[ \cos(x) = -\frac{1}{14} \][/tex]
Now, find x using the inverse cosine [tex](arccos)[/tex] function:
[tex]\[ x = \cos^{-1}\left(-\frac{1}{14}\right) \]\\\\x=cos ^{-1} (-0.0714285714285714)\\Calculate~ \( x \):\\ x = 94.1^\circ[/tex]
Therefore, x is approximately [tex]\( 94.1^\circ \)[/tex].
Conclusion:
The correct option is:
C) 94.1 degrees
This corresponds to the calculated angle x using the cosine rule and solving for x.
Answer:
Option C
Step-by-step explanation:
By applying cosine rule in the given triangle,
BC² = AB² + AC² - 2(AB)(AC)cosA
(11)² = 8² + 7² - 2(8)(7)cosx
121 = 64 + 49 - 112cos(x)
cos(x) = -[tex]\frac{8}{112}[/tex]
x = [tex]\text{cos}^{-1}(-\frac{1}{14})[/tex]
x = 94.1°
Therefore, Option C will be the correct option.