To solve the problem, we need to determine the angle $\theta$ in the given right triangle.

Given:

• The length of the hypotenuse is $16.5$ meters.
• The length of the side adjacent to the angle $\theta$ is $15.1$ meters.

Solution:

In a right triangle, the cosine of angle $\theta$ is given by the ratio of the length of the adjacent side to the hypotenuse: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{15.1}{16.5}$

Let's calculate $\theta$.

$\cos(\theta) = \frac{15.1}{16.5} \approx 0.9152$

Now, we take the arccosine (inverse cosine) to find $\theta$:

$\theta = \cos^{-1}(0.9152) \approx 23.73^\circ$

Final Answer:

The angle $\theta$ is approximately $23.73^\circ$.

Would you like more details or have any questions about this problem?

Here are five related questions to explore further:

1. How would you find the length of the opposite side in this triangle?
2. What if the hypotenuse were longer; how would that affect $\theta$?
3. Can you solve for $\theta$ using the sine or tangent functions?
4. What is the area of this triangle given the lengths of two sides?
5. How would the calculation change if the given side lengths were in a different unit?

Tip: Always double-check which side corresponds to the hypotenuse, opposite, and adjacent when using trigonometric ratios.