SOLUTION: Two fire towers F and T are 30 km apart, F is due north of T. A fire at point G is observed from both towers. A watcher from F observes the bearing of the fire to be S 54°E and fro

Algebra ->  Trigonometry-basics -> SOLUTION: Two fire towers F and T are 30 km apart, F is due north of T. A fire at point G is observed from both towers. A watcher from F observes the bearing of the fire to be S 54°E and fro      Log On


   

Question 1122325: Two fire towers F and T are 30 km apart, F is due north of T. A fire at point G is observed from both towers. A watcher from F observes the bearing of the fire to be S 54°E and from T the bearing of the same fire is N 31°E. Find the distance of the fire from A.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.