Answer:
16.27 mm² (2 d.p.)
Step-by-step explanation:
Area of a triangle
[tex]\boxed{ A=\dfrac{1}{2}ab \sin C}[/tex]
where:
- C is the angle.
- a and b are the sides enclosing the angle.
Given:
- a = 11 mm
- b = 14 mm
- C = θ = 12.2°
Substitute the given values into the formula and solve for A:
[tex]\begin{aligned}A & = \dfrac{1}{2}ab \sin C\\\\\implies A & = \dfrac{1}{2}(11)(15) \sin (12.2^{\circ})\\& =82.5\sin (12.2^{\circ})\\& = 16.2720093...\\& = 16.27 \sf \;mm^2\; (2 \:d.p.)\end{aligned}[/tex]
Therefore, the area of the triangle is 16.27 mm² (2 d.p.).
