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We are given a triangle \( \triangle ABC \) with:

- \( BD = 30 \, m \)
- \( \angle DBC = 90^\circ \)
- \( \angle ACB = 40^\circ \)

We are tasked with calculating the following sides:

- \( AB \)
- \( BC \)
- \( AD \)
- \( DC \)
- \( AC \)

### Step-by-Step Solution:

1. **Interpretation:**
   - \( BD \) is perpendicular to \( AC \), so \( \triangle BDC \) is a right triangle.
   - \( \angle ACB = 40^\circ \).

2. **Using Trigonometry:**
   Since \( \triangle ABC \) is a triangle with one known angle \( \angle ACB = 40^\circ \), we can calculate the unknown sides using trigonometric ratios. First, we need to calculate the length of \( BC \) (adjacent side to \( \angle ACB \)).

3. **Calculate \( BC \):**
   Using trigonometric identities:
   \[
   \tan(40^\circ) = \frac{BD}{BC}
   \]
   Solving for \( BC \):
   \[
   BC = \frac{BD}{\tan(40^\circ)} = \frac{30}{\tan(40^\circ)}
   \]

4. **Use Pythagoras Theorem in \( \triangle BDC \):**
   After calculating \( BC \), we can use Pythagoras theorem in \( \triangle BDC \) to find \( DC \).

Let me calculate these values now.We have calculated the following:

- \( BC = 35.75 \, \text{m} \)
- \( DC = 19.45 \, \text{m} \)

Next, let's calculate the remaining sides \( AB \), \( AD \), and \( AC \).

1. **Calculate \( AB \):**
   Using the sine rule or cosine rule based on the angles, we will calculate \( AB \).

2. **Calculate \( AC \):**
   Using the trigonometric ratios, we can determine \( AC \), which will be the hypotenuse in \( \triangle ABC \).

Let me compute these now.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, based on the previous calculations:

- \( BC = 35.75 \, \text{m} \)
- \( DC = 19.45 \, \text{m} \)

Would you like help finishing the rest of the problem manually, or do you have any questions so far?

Here are some related questions to think about:
1. How can we use the sine rule to calculate unknown sides in triangles?
2. What is the relationship between the angles and sides in a right triangle?
3. How do we apply the Pythagorean theorem in different right triangles?
4. Can you find \( AB \) and \( AC \) using trigonometric functions like sine and cosine?
5. What other methods can be used to solve a triangle with known angles and sides?

**Tip:** Always remember to use appropriate trigonometric identities depending on the known angles and sides to solve for unknown parts of the triangle.

If BD = 30m, calculate AB, BC, AD, DC, and AC.

Solve for AB, BC, AD, DC, and AC in a triangle using trigonometric identities and the Pythagorean theorem. With BD = 30m and angle ACB = 40°, learn how to apply the tangent function and right triangle properties to find the unknown sides.

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