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To find the length of the support rod connecting the top of the tent pole to the ground, we can use trigonometry, specifically the sine function.
Given:
- Length of the tent pole (height perpendicular to the ground) = 229 cm
- Angle between the support rod and the ground = 65°
We need to find the length \( L \) of the support rod.
Using the sine function:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case, the opposite side to the angle of 65° is the length of the tent pole (229 cm), and the hypotenuse is the length of the support rod \( L \).
So,
\[ \sin(65^\circ) = \frac{229}{L} \]
To find \( L \), rearrange the equation:
\[ L = \frac{229}{\sin(65^\circ)} \]
Now, calculate \( L \):
\[ L = \frac{229}{\sin(65^\circ)} \]
Using a calculator:
\[ \sin(65^\circ) \approx 0.9063 \]
Therefore,
\[ L = \frac{229}{0.9063} \approx 252.70 \]
Rounded to the nearest integer, the length of the support rod \( L \) is approximately \( \boxed{253} \) centimetres.