To find the area of a triangle given two sides and the included angle, you can use the formula:
\[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \]
where \( a \) and \( b \) are the lengths of the two sides, and \( C \) is the included angle in degrees.
In this case:
- \( a = 14 , m \)
- \( b = 20 , m \)
- \( C = 120^\circ \)
We first need to calculate \( \sin(120^\circ) \). The sine of \( 120^\circ \) can be calculated as:
\[ \sin(120^\circ) = \sin(180^\circ - 60^\circ) = \sin(60^\circ) = \frac{\sqrt{3}}{2} \]
Now substituting the values into the area formula:
\[ \text{Area} = \frac{1}{2} \times 14 \times 20 \times \sin(120^\circ) \] \[ = \frac{1}{2} \times 14 \times 20 \times \frac{\sqrt{3}}{2} \] \[ = \frac{1}{2} \times 14 \times 20 \times 0.866 \] \[ = \frac{1}{2} \times 280 \times 0.866 \] \[ = 140 \times 0.866 \] \[ \approx 121.24 , m^2 \]
Thus, the area of the triangle is approximately 121.24 m².
Among the options provided, the correct response is 121.24 m².
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