Calculate the size of the angle θ (theta) in this field. Give your answer to the nearest degree.

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 degrees
A right-angled triangle with one side of 50m (adjacent) and a hypotenuse of 60m. 

To find the angle \(\theta\) in a right-angled triangle when you are given the adjacent side and the hypotenuse, we can use the **cosine** function. 

The formula for the cosine of an angle is:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

### Given:
- Adjacent side = 50 m
- Hypotenuse = 60 m

### Calculation:
\[
\cos(\theta) = \frac{50}{60} = 0.8333
\]

Now, to find \(\theta\), we take the inverse cosine (also called arccos) of 0.8333:

\[
\theta = \cos^{-1}(0.8333)
\]

Using a calculator:

\[
\theta \approx 33.56^\circ
\]

Rounding to the nearest degree:

\[
\theta \approx 34^\circ
\]

### Final Answer:
\(\theta = 34^\circ\)

Would you like more details or have any questions?

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Here are 5 related questions you might explore:
1. What if the hypotenuse were shorter, say 55 m, how would \(\theta\) change?
2. How do you calculate the opposite side in this triangle?
3. What if the adjacent side were unknown, how would you find it with only \(\theta\) and the hypotenuse?
4. Can you determine the area of the triangle given its sides?
5. How does the tangent of \(\theta\) relate to this triangle?

**Tip**: Always double-check your calculations by reapplying trigonometric functions to see if the triangle's other properties (like the opposite side) match the expected ratios.

Calculate the size of the angle θ (theta) in this field. Give your answer to the nearest degree. A right-angled triangle with one side of 50m (adjacent) and a hypotenuse of 60m.

Find the size of angle θ in a right-angled triangle where the adjacent side is 50 meters and the hypotenuse is 60 meters. This problem uses trigonometric concepts like cosine and inverse cosine to solve for θ, suitable for students in Grades 9-11.

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