To calculate the length $x$, we can use the sine rule since we are dealing with a non-right triangle.

The sine rule states: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$ Where:

• $a, b, c$ are the sides of the triangle.
• $A, B, C$ are the opposite angles to the respective sides.

Step 1: Identify the given values

• $a = 11 \, \text{cm}$ (side opposite the 60° angle).
• $A = 60^\circ$ (angle opposite side $a$).
• $B = 44^\circ$ (angle opposite $x$).

Step 2: Find the third angle $C$

The angles of a triangle add up to $180^\circ$. Thus: $C = 180^\circ - 60^\circ - 44^\circ = 76^\circ$

Step 3: Apply the sine rule

The sine rule relates the sides and angles: $\frac{x}{\sin 44^\circ} = \frac{11}{\sin 60^\circ}$

We rearrange to solve for $x$: $x = \frac{11 \cdot \sin 44^\circ}{\sin 60^\circ}$

Step 4: Use a calculator to evaluate the sines

• $\sin 44^\circ \approx 0.694$
• $\sin 60^\circ \approx 0.866$

Substitute these values: $x = \frac{11 \cdot 0.694}{0.866}$

$x \approx \frac{7.634}{0.866} \approx 8.8$

Final Answer:

The length $x$ is approximately 8.8 cm (to 2 significant figures).

Let me know if you would like further clarifications! Here are 5 related questions:

1. How do you derive the sine rule for any triangle?
2. What is the cosine rule, and when is it used?
3. How do you find the area of a triangle using sine?
4. How do you calculate a missing angle in a triangle using the sine rule?
5. What happens if two angles are the same in a triangle?

Tip: Always check that the angles add up to $180^\circ$ before applying trigonometric rules.