QUESTION ONE Find the value of $$ T $$ in the formula $$ T=\pi \sqrt{\frac{h \sin x}{g}} $$ when $$ h-2,5, g=9,81, x=75^{\circ} $$, (a) giving your answer correct to four decimal places.

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To find the value of $$ T $$ in the formula

$$
T = \pi \sqrt{\frac{h \sin x}{g}},
$$

we need to substitute the given values: $$ h = 2.5 $$, $$ g = 9.81 $$, and $$ x = 75^\circ $$.

First, we need to calculate $$ \sin(75^\circ) $$. Using a calculator, we find:

$$
\sin(75^\circ) \approx 0.9659.
$$

Now we can substitute the values into the formula:

$$
T = \pi \sqrt{\frac{2.5 \cdot 0.9659}{9.81}}.
$$

Calculating the numerator:

$$
2.5 \cdot 0.9659 \approx 2.41475.
$$

Now, we divide by $$ g $$:

$$
\frac{2.41475}{9.81} \approx 0.246.
$$

Next, we take the square root:

$$
\sqrt{0.246} \approx 0.496.
$$

Finally, we multiply by $$ \pi $$:

$$
T \approx \pi \cdot 0.496 \approx 1.558.
$$

Thus, rounding to four decimal places, we have:

$$
T \approx 1.5580.
$$

Therefore, the value of $$ T $$ is

$$
\boxed{1.5580}.
$$
$$ T \approx 1.5580 $$.

QUESTION ONE Find the value of \( T \) in the formula \( T=\pi \sqrt{\frac{h \sin x}{g}} \) when \( h-2,5, g=9,81, x=75^{\circ} \), (a) giving your answer correct to four decimal places.

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