The problem refers to triangle ABC. Find the area of the triangle. Round to three significant digits. B = 9° 20', C = 80° 40', b = 2.92 ft

Answer:Area of the triangle is 25.9 feet²Step-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