In triangle ABC:

A = 38°45' , b = 67 , c = 85

The area of the given triangle: 

Area: T = 1782.317

A   = 1/2 x 67 x 85 sin 38•75 ° units²

A   = 1768•2 units²

Area of triangle: 0.5*b*c*sin(A) in square units

Use Law of Cosine.

a²= 67² + 85² -2*67*85cos(38° 45'); a≈ 53.2

Use Heron's formula.

s= (67 + 85 + 53.2)/2= 102.6

area= √[s(s - 67)(s - 85)(s - 53.2)]≈ 1782 units²

The area of the triangle given

A = 38°45' , b = 67 , c = 85:

Height: 66.99

Area of the triangle: 

1/2(53.21)(66.99) = 1782.26895

area = (1/2)bcsin(A)