Answer:
Area of the triangle is 25.9 feet²
Step-by-step explanation:
* Lets explain how to solve the problem
- In Δ ABC
∵ m∠ B = 9° 20' = 9 + 20/60 = (28/3)°
∵ b = 2.92 feet
- b is the side opposite to angle B
∵ m∠ C = 80° 40' = 80 + 40/60 = (242/3)°
- Lets find c the side opposite to angle C by sing the sine rule
∵ [tex]\frac{b}{sinB}=\frac{c}{sinC}[/tex]
∴ [tex]\frac{2.92}{sin(28/3)}=\frac{c}{sin(242/3)}[/tex]
- By using cross multiplication
∴ [tex]c=\frac{2.92(sin(242/3)}{sin(28/3)}=17.77[/tex]
- The area of the triangle = 1/2 (b)(c)sin∠A
∵ The sum of the interior angles of a triangle is 180°
∴ m∠ A + m∠ B + m∠ C = 180°
∵ m∠ B = (28/3)°
∵ m∠ C = (242/3)°
∴ m∠ A + 28/3 + 242/3 = 180
∴ m∠ A + 90° = 180° ⇒ subtract 90 from both sides
∴ m∠ A = 90°
∴ Area of the triangle = 1/2 (2.92)(17.77) sin(90)
∵ sin(90) = 1
∴ Area of the triangle = 1/2 (2.92)(17.77) = 25.9 feet²
* Area of the triangle is 25.9 feet²
