To solve for angle $\theta$ in the triangle, we will use trigonometric ratios. Here's the approach:

Step 1: Identify the triangle and values

• Opposite side to $\theta$: $8 \, \text{ft}$
• Adjacent side to $\theta$: $10 \, \text{ft}$

Step 2: Use the tangent function

The tangent of angle $\theta$ is the ratio of the opposite side to the adjacent side: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ Substitute the values: $\tan(\theta) = \frac{8}{10} = 0.8$

Step 3: Solve for $\theta$

To find $\theta$, take the inverse tangent ($\tan^{-1}$) of $0.8$: $\theta = \tan^{-1}(0.8)$

Using a calculator: $\theta \approx 38.66^\circ$

Step 4: Round to the nearest degree

$\theta \approx 39^\circ$

Final Answer:

$\theta \approx 39^\circ$

Do you need further clarification or details? Here are some questions you might consider:

1. What is the significance of using tangent over sine or cosine?
2. How can I solve similar problems without a calculator?
3. Can we confirm this answer using another trigonometric function?
4. How does the precision of values affect the result?
5. How would this process differ for an obtuse triangle?

Tip: Always double-check which side is the opposite, adjacent, or hypotenuse when using trigonometric functions!