Find the area $\mathrm{K}$ of the triangle.
\[
a=8, c=1, B=120^{\circ}
\]

Answer

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Answer

$\boxed{3.464101615137755}$ is the final answer.

Steps

Step 1 ：We are given a triangle with side lengths a = 8, c = 1, and the angle B = 120 degrees between them. We are asked to find the area of the triangle.

Step 2 ：The formula to find the area of a triangle when two sides and the included angle are known is $K = \frac{1}{2}ac\sin B$.

Step 3 ：Substituting the given values into the formula, we get $K = \frac{1}{2} * 8 * 1 * \sin 120$.

Step 4 ：Calculating the above expression, we find that the area of the triangle is approximately 3.464101615137755.

Step 5 ：$\boxed{3.464101615137755}$ is the final answer.

Find the area $\mathrm{K}$ of the triangle.\[a=8, c=1, B=120^{\circ}\]

Answer

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Find the area $\mathrm{K}$ of the triangle.
\[
a=8, c=1, B=120^{\circ}
\]