To calculate the angle $\theta$ in the triangle, we can use trigonometric functions. Since the triangle has a right angle, we apply the tangent function.

Step-by-Step Solution:

1. Label the triangle:

   • The side opposite $\theta$: $53.4 \, \text{m}$
   • The side adjacent to $\theta$: $79.6 \, \text{m}$

2. Use the tangent function: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ Substituting the given values: $\tan(\theta) = \frac{53.4}{79.6}$

3. Calculate the ratio: $\tan(\theta) = 0.6702$

4. Find $\theta$ using the inverse tangent: $\theta = \tan^{-1}(0.6702)$ Using a calculator: $\theta \approx 33.8^\circ$

Final Answer:

The size of angle $\theta$ is 33.8° (to 1 decimal place).

Do you want me to explain any step further? Let me know!

Here are 5 related questions for you to explore:

1. How do we identify when to use sine, cosine, or tangent in a triangle?
2. How can the Pythagorean theorem help in right-angled triangles?
3. What is the process for solving triangles without a right angle?
4. How do you convert angles between degrees and radians?
5. How do you calculate the area of this triangle using trigonometry?

Tip: Always use inverse trigonometric functions when you need to find the angle in right triangles.