Answer :

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.

Thanks for taking the time to read Solve the triangle for x View the attachment A 39 4 degrees B 46 5 degrees C 94 1 degrees D 105 9 degrees. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

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.