Answer:
15.8 cm²
Step-by-step explanation:
Please see attached photo for diagram.
We'll begin by calculating the angle A. This can be obtained as follow:
B = 56°
C = 78°
A =?
A + B + C = 180 (Sum of the angle in triangle)
A + 56 + 78 = 180
A + 134 = 180
Collect like terms
A = 180 – 134
A = 46°
Next, we shall determine the value of b by using the sine rule. This can be obtained:
Side opposite angle C (c) = 7.2 cm
Angle C = 78°
Angle B = 56°
Side opposite angle B (b) =?
b/Sine B = c/sine C
b/Sine 56 = 7.2/Sine 78
Cross multiply
b × Sine 78 = 7.2 × Sine 56
Divide both side by Sine 78
b = 7.2 × Sine 56 / Sine 78
b = 6.1 cm
Finally, we shall determine the area of the triangle. This can be obtained as follow:
Side opposite angle C (c) = 7.2 cm
Side opposite angle B (b) = 6.1 cm
Angle A = 46°
Area (A) =?
A = ½bcSineA
A = ½ × 6.1 × 7.2 × Sine 46
A = 15.8 cm²
Therefore, the area of the triangle is 15.8 cm²
