SOLUTION: Two fire towers are 30 km apart. A fire is spotted from the distant West tower at 18° N of E while the same fire is spotted from the East tower at 41° N of W. How much closer is

Algebra ->  Trigonometry-basics -> SOLUTION: Two fire towers are 30 km apart. A fire is spotted from the distant West tower at 18° N of E while the same fire is spotted from the East tower at 41° N of W. How much closer is       Log On


   

Question 1165352: Two fire towers are 30 km apart. A fire is spotted from the distant West tower at 18° N of E while the same fire is spotted from the East tower at 41° N of W. How much closer is the East Tower to the fire than the West tower?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two fire towers are 30 km apart.
A fire is spotted from the distant West tower at 18° N of E while the same fire is spotted from the East tower at 41° N of W.
How much closer is the East Tower to the fire than the West tower?
:
this forms a simple triangle ABC where AB is the base of 30 km,
A is the west tower with an angle of 18
B is the east tower with an angle of 41
:
a = east tower dist to fire
b = west tower dist to fire
:
Find the 3rd angle which is at the fire
180 - 18 - 41 = 121 degrees
:
Use the law of sines
a%2Fsin%2818%29 = 30%2Fsin%28121%29
Cross multiply
sin(121)a = 30*sin(18)
then
a = %2830%2Asin%2818%29%29%2Fsin%28121%29
a = 10.82 mi east tower to fire
and
b%2Fsin%2841%29 = 30%2Fsin%28121%29
Cross multiply
sin(121)a = 30*sin(41)
then
b = %2830%2Asin%2841%29%29%2Fsin%28121%29
b = 22.96 mi west tower to fire
:
" How much closer is the East Tower to the fire than the West tower?"
22.96 - 10.82 = 12.14 mi is the east tower closer than the west tower