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two fire look-out stations are 20 miles apart with station B directily east of station A……?

two fire look-out stations are 20 miles apart with station B directly east of station A. both station spot a fire. the bearing of the fire from staion A is N60degree E and the bearing of the fire station B is N40degreeW. how far is it from station A to the fire?

13.054 miles

use the law of sines.

since its a triangle, and two angles are 40 and 60, the other is 80, and the 80 is opposite of the 20 mile length and x is across from the 40 degree angle, so:

20          x
—–   =  —–
sin80    sin40

x = (20sin40)/sin80 = 13.054072893322786045931334929227408159984972912637224510550 ….or 13.054 miles

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One Response to “two fire look-out stations are 20 miles apart with station B directily east of station A……?”

  1. 13.054 miles

    use the law of sines.

    since its a triangle, and two angles are 40 and 60, the other is 80, and the 80 is opposite of the 20 mile length and x is across from the 40 degree angle, so:

    20          x
    —–   =  —–
    sin80    sin40

    x = (20sin40)/sin80 = 13.054072893322786045931334929227408159984972912637224510550 ….or 13.054 miles
    References :

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