To solve the expression [tex]\( \sqrt{\frac{2.5 \times \sin 43^{\circ}}{8.2^2-50.5}} \)[/tex], follow these steps:
1. Calculate the sine of 43 degrees:
[tex]\[
\sin 43^\circ \approx 0.682
\][/tex]
2. Multiply this by 2.5:
[tex]\[
2.5 \times \sin 43^\circ \approx 2.5 \times 0.682 = 1.705
\][/tex]
So, the numerator is approximately 1.705.
3. Calculate the denominator:
[tex]\[
8.2^2 - 50.5 = 67.24 - 50.5 = 16.74
\][/tex]
4. Divide the numerator by the denominator:
[tex]\[
\frac{1.705}{16.74} \approx 0.102
\][/tex]
5. Take the square root of the result:
[tex]\[
\sqrt{0.102} \approx 0.319
\][/tex]
6. Round the result to 3 significant figures:
[tex]\[
\approx 0.319
\][/tex]
Therefore, the value of [tex]\( \sqrt{\frac{2.5 \times \sin 43^{\circ}}{8.2^2-50.5}} \)[/tex] rounded to 3 significant figures is [tex]\( \boxed{0.319} \)[/tex].
