College

Thank you for visiting Solve the triangle for x View the attachment A 39 4 degrees B 46 5 degrees C 94 1 degrees D 105 9 degrees. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Solve the triangle for x.

(View the attachment)


A. 39.4(degrees)

B. 46.5(degrees)

C. 94.1(degrees)

D. 105.9(degrees)

Solve the triangle for x View the attachment A 39 4 degrees B 46 5 degrees C 94 1 degrees D 105 9 degrees

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.

Thank you for reading the article 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 information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

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.

Other Questions