https://file.aiquickdraw.com/mathbot/file/1726908276882qnga3v0a.jpg

To solve for \( x \) using the cosine rule, we'll use the formula:

\[
x^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]

Where:
- \( a = 55 \) cm,
- \( b = 50 \) cm,
- \( C = 61^\circ \).

Now, let's calculate:

\[
x^2 = 55^2 + 50^2 - 2(55)(50) \cdot \cos(61^\circ)
\]

I'll compute that for you.The value of \( x \) is approximately \( 53.47 \, \text{cm} \), matching the provided answer in the image.

Do you want any further details or have any questions? Here are five related questions to expand your understanding:

1. How can the cosine rule be derived from the Pythagorean theorem?
2. When should you use the cosine rule versus the sine rule?
3. Can the cosine rule be applied to obtuse triangles, and how does that affect the calculation?
4. How would the solution change if angle \( C \) was larger than \( 90^\circ \)?
5. What other trigonometric functions are useful in non-right triangles?

**Tip:** Always ensure the angle is between the two given sides when applying the cosine rule, as it ensures the correct relation between the sides and angle.

Find the value of x using cosine rule with sides 55 cm and 50 cm, and an angle of 61°.

Learn how to find the unknown side of a triangle using the cosine rule. This problem features two known sides (55 cm and 50 cm) and an angle of 61°. Suitable for students in Grades 9-11 studying trigonometry.

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