https://file.aiquickdraw.com/mathbot/file/17299480337947ezomocp.jpg

Let's solve the two problems labeled **(a)** and **(b)** one by one.

### Diagram (a)
In diagram (a), we are given:
- Triangle \( ABC \) with:
  - \( AB = 8 \) cm
  - \( BD = 5 \) cm
  - Angle \( \angle ABD = 50^\circ \)

The goal is to find the length \( x \), which corresponds to the side \( AD \).

**Solution for (a):**
To solve this, we can use the **Law of Sines**, which states:

\[
\frac{AB}{\sin(\angle ACD)} = \frac{AD}{\sin(\angle ABD)}
\]

However, to directly solve it, further details of the angle values are required which might not be given here.



Find x in each of the following diagrams.

Learn how to find the unknown side lengths x in two triangles using the Law of Sines. Diagrams illustrate the setup with given side lengths and angles, offering a step-by-step guide for applying trigonometric methods. Suitable for high school students in Grades 10-12.

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