Let h be the height of the mountain C.

Angle of elevation of C from B is 19.3 degrees. x is the distance between B and C. So

tan(19.3) = (h-1575.2)/x.....(1)

Angle of elevation of C from A is 16.8 degrees.So

tan(16.8) = (h-1240.8)/(1742.6 + x)......(2)

Substitute the value of x from equation 1 in eq.(2) and solve for h.