Area from two sides and the included angle

Problem

Work out the area of a triangle with sides $b=5$, $c=6$ and included angle $\widehat{A}=120°$.

Solution

Apply the trigonometric formula for the area with the angle included between the two known sides: $S = \tfrac12\,bc\sin\widehat{A} = \tfrac12\cdot 5\cdot 6\cdot\sin 120° = 15\cdot\frac{\sqrt{3}}{2} = \frac{15\sqrt{3}}{2} \approx \boxed{12{,}99}.$

Links

Topics: Triangle trigonometry
Concepts: Triangle area
Functions: Sine
Skills: Calculating · Using formulae
Exercise type: Geometric problem