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The problem shows a right triangle where:

- One angle is 35 degrees.
- The opposite side to the 35-degree angle is labeled as \( b = 8 \, \text{m} \).
- We are asked to find the adjacent side, labeled as \( a \).

Since we have an angle and the length of the side opposite to it, we can use the **tangent function**:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

In this case:

\[
\tan(35^\circ) = \frac{b}{a}
\]

Rearranging to solve for \( a \):

\[
a = \frac{b}{\tan(35^\circ)}
\]

Now, let's compute \( a \).The length of side \( a \) is approximately \( 11.43 \, \text{m} \). Therefore, the closest answer is \( 11 \, \text{m} \).

Would you like any further details on the calculation, or have additional questions?

Here are five related questions to expand your understanding:
1. How can we calculate the length of the hypotenuse \( c \) in this triangle?
2. What is the sine and cosine of the 35-degree angle in this triangle?
3. How can we use the Pythagorean theorem to verify this solution?
4. How would the calculation change if we were given the hypotenuse instead of side \( b \)?
5. What are some real-life applications of right triangle trigonometry?

**Tip:** When solving trigonometry problems, always remember to keep your calculator in the correct mode (degrees or radians) based on the problem context.

If the angle is 35 degrees, and b = 8 m, then a = ?

Explore how to find the adjacent side length in a right triangle using the tangent function when one angle is 35 degrees and the opposite side is 8 meters. This guide provides step-by-step solutions and discusses related trigonometric concepts.

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