Question 1122325
this forms a triangle FGT.


angle GFT = 54 degrees.
angle GTF = 31 degrees.


because the sum of the angle of a triangle is 180 degrees, then .....


angle FGT = 95 degrees.


the towers are 30 kilometers apart.


therefore FT = 30


use the law of sines to find the length of the other 2 sides of the triangle.


law of sines says that .....


a/sin(A) = b/sin(B) = c/sin(C)


this gets you FG / sin(31) = 30 / sin(95).


cross multiply to get FG * sin(95) = 30 * sin(31).


solve for FG to get FG = 30 * sin(31) / sin(95) = 15.5101631 kilometers.


this also gets you GT / sin(54) = 30 / sin(95).


cross multiply to get GT * sin(95) = 30 * sin(54).


solve for GT to get GT = 30 * sin(54) / sin(95) = 24.36321924 kilometers.


you want the distance of the fire from A?


there is no point A.


the fire is at point G.


the distance of the fire from point F is 15.5101631 kilometers.


the distance from point T is 24.36321924 kilometers.