Law of sines: length-of-a/SIN(angle A) =length-of-c/SIN(angle C)
 h is perpendicular to line c

a=SIN A *(c/SIN C)

Where in a 90 degree triangle h/a= SIN B then h=SIN B * a

substitute the definition of "a" from above then:

h=SIN B*a=SIN B * (SIN A * c/SIN C)

Where angles A+B+C=180 then C= 180-A-B

h=SIN B * SIN A * c / SIN (180-A-B)

h=SIN A * SIN B * c / SIN (180-A-B)

The aircraft's altitude (h) can now be solved because we know angles A and B and the length of c.