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Okay, let’s solve for x in the triangle using the Law of Sines.
We have a triangle with one side of length 13 cm, an angle of 38^\circ opposite that side, an angle of 100^\circ and we want to find the length x of the side opposite the 100^\circ angle.
Using the Law of Sines, we have:
\frac{x}{\sin(100^\circ)} = \frac{13}{\sin(38^\circ)}Now, we solve for x:
x = \frac{13 \cdot \sin(100^\circ)}{\sin(38^\circ)}Using a calculator, we find that \sin(100^\circ) \approx 0.9848 and \sin(38^\circ) \approx 0.6157 .
Therefore, x = \frac{13 \cdot 0.9848}{0.6157} \approx \frac{12.8024}{0.6157} \approx 20.79
Rounding to one decimal place, we get x \approx 20.8
Therefore, the value of x is approximately 20.8 cm.
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