Explanation:
remember, the sum of all angles in a triangle is always 180°.
the law of sine :
a/sinA = b/sinB = c/sinC
with a, b, c being the sides of the triangle, A,B,C being the corresponding opposite angles.
so, we can get the angle A first, and then we can calculate angle C.
14/sin(109) = 9/sinA
14×sinA = 9×sin(109)
sinA = 9×sin(109)/14 = 0.60783337...
angle A = 37.43300585...°
A + B + C = 180
37.43300585...° + 109° + C = 180
angle C = 33.56699415...° ≈ 33.6°
the area of a triangle is
baseline × height / 2
let's use AC (14 in) as baseline. then the height from B down to AC is the sine of C times the radius of the trigonometric circle (9 in) with center at C.
height = sinC × 9 = 4.976204798... in
the triangle area is then
14 × 4.976204798... / 2 = 34.83343358... in²
≈ 34.8 in²