Answer:
9.8 in²
Step-by-step explanation:
If A, B and C are the angles of a triangle and a, b, c are the repective sides opposite the angles, then the area of the triangle is given as:
Area = (1/2)absin(C)
In ΔQRS, the area is:
Area = (1/2)rqsin(S)
∠S + ∠Q + ∠R = 180° (sum of angles in a triangle)
∠S + 40 + 101 = 180
∠S = 39°
Using sine rule to find q:
[tex]\frac{q}{sinQ} =\frac{r}{sinR} \\\\\frac{q}{sin40}=\frac{6.9}{sin101} \\\\q=\frac{6.9*sin40}{sin101} =4.52 \ inches\\\\Area\ of\ triangle \ QRS=\frac{1}{2}rqsin(S) =\frac{1}{2}*6.9*4.52*sin(39)=9.8\ in^2[/tex]
