This problem requires us to calculate the value of $x$, which represents the angle at the base of the triangle. Since this involves a right triangle, trigonometric functions like sine, cosine, or tangent are appropriate. Here's how we'll solve it step by step:

Step 1: Identify given values and relationship

The given triangle has:

• Adjacent side to $x$: $6 \, \text{cm}$,
• Opposite side to $x$: $4 \, \text{cm}$,
• Hypotenuse: $8 \, \text{cm}$.

Using the tangent function is appropriate because: $\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$

Step 2: Apply the tangent formula

$\tan(x) = \frac{4}{6} = 0.6667$

Step 3: Calculate $x$ using the arctangent

Use the arctangent function to find $x$: $x = \tan^{-1}(0.6667)$

Using a calculator: $x \approx 33.7^\circ$

Final Answer:

The value of $x$ is 33.7°, correct to 1 decimal place.

Would you like further clarification or a breakdown of the trigonometric functions used?

Related Questions:

1. What is the role of the hypotenuse in solving trigonometric problems like this?
2. Can we use sine or cosine here instead of tangent? How?
3. How does rounding affect the accuracy of trigonometric calculations?
4. What is the relationship between tangent, sine, and cosine?
5. How would you solve this problem without a calculator?

Tip:

For trigonometry, always ensure you are working in the correct unit (degrees or radians) as per the problem's requirement.