Towers a and b are located 5 miles apart. a ranger spots a fire at a 42-degree angle from tower a. another fire ranger spots the same fire at a 64-degree angle from tower b. to the nearest tenth of a mile, how far from tower b is the fire?
3.5 mi
3.7 mi
6.7 mi
7.2 mi

4.67 miles

step-by-step explanation:

given:

distance between towers, x= 5 miles

angle between tower a and fire, a= 42 degrees

angle between tower a and fire, b= 64 degrees

let y be the distance between tower a and fire

let z be the distance between tower b and fire

now by applying asa property of triangles, we have:

third angle= 180-42-64

                  =74 degrees

applying law of sines

a/sina=b/sinb

x/sin74=y/sin42

y=5sin42/sin74

y=3.34/0.9

y=3.48

x/sin74=z/sin64

z=5sin64/sin74

z=4.49/0.96

z=4.67!