In triangle , suppose that , , andCompute the area of triangle . [3 points]\
[THOUGHT] Use the formula for area with two sides and the included angle: (\text{Area}=\frac12 \cdot AB \cdot AC \cdot \sin(\angle BAC)). Given (\cos(\angle BAC)=-\frac35), we get (\sin(\angle BAC)=\sqrt{1-\cos^2}=\sqrt{1-\frac{9}{25}}=\frac45) (positive since the angle is between (0^\circ) and (180^\circ)). Then compute the area and verify with Python. [/THOUGHT] [PYTHON] import sympy as sp
AB = 5 AC = 6 cosA = -sp.Rational(3,5) sinA = sp.sqrt(1 - cosA**2) # positive sine for an angle in (0, pi) area = sp.Rational(1,2) * AB * AC * sinA print(sinA) print(area) [/PYTHON]
[THOUGHT] The computed sine is (4/5), so the area is (\frac12\cdot 5\cdot 6\cdot \frac45=12). \boxed{12}