A decorative pillow is being sewn and the pattern for the material to make the pillow canbe modeled by A ABC, in which AC = 10 inches, AB = 9 inches, BC = 15 inches, andWhat is the area of the pattern, rounded to the nearest tenth?The area of the pattern issquare inches

Answer:The area of the pattern is 43.6 inches²Step-by-step explanation:* Lets explain how to solve the problem- A decorative pillow can be modeled by Δ ABC- In Δ ABC: AB = 9 inches , BC = 15 inches , AC = 10 inches- To find the area of the triangle we can use the rule:   A = 1/2 × (AB) × (BC) × sin∠B- We will use the cosine rule to find the measure of angle B∵ [tex]cos(B)=\frac{(AB)^{2}+(BC)^{2}-(AC)^{2}}{2(AB)(BC)}[/tex]∵ AB = 9 , BC = 15 , AC = 10 ∴ [tex]cos(B)=\frac{9^{2}+15^{2}-10^{2}}{2(9)(15)}=\frac{81+225-100}{270}=\frac{206}{270}=\frac{103}{135}[/tex]∴ m∠B = [tex]cos^{-1}\frac{103}{135}=40.27[/tex]°* Lets find the area of the triangle∴ The area = 1/2 × (9) × (15) × sin(40.27) = 43.6 inches²* The area of the pattern is 43.6 inches²