Question

A decorative pillow is being sewn and the pattern for the material to make the pillow can

be modeled by A ABC, in which AC = 10 inches, AB = 9 inches, BC = 15 inches, and

What is the area of the pattern, rounded to the nearest tenth?
The area of the pattern is
square inches

Answer 1

The area of the pattern is 43.6 inches²

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

∵
`cos(B)=((AB)^(2)+(BC)^(2)-(AC)^(2))/(2(AB)(BC))`

∵ AB = 9 , BC = 15 , AC = 10

∴
`cos(B)=(9^(2)+15^(2)-10^(2))/(2(9)(15))=(81+225-100)/(270)=(206)/(270)=(103)/(135)`

∴ m∠B =
`cos^(-1)(103)/(135)=40.27`°

* 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