Question 1200660
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Answer: <font color=red size=4>161.2984 meters (approximate)</font>


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Explanation:


The given angles are
A = 37 degrees
B = 48 degrees 


Let's find angle C
A+B+C = 180
C = 180-A-B
C = 180-37-48
C = 95 degrees


The interior angles of the triangle are
A = 37 degrees
B = 48 degrees
C = 95 degrees


The shortest side is opposite the smallest angle.
The longest side is opposite the largest angle.


Since C = 95 is the largest angle, we have c = 267 as the longest side.


Side 'a' is the shortest side, opposite the smallest angle (A = 37)


Diagram
{{{
drawing(400,300,-5,5,-7,3,

locate(0.34,-2.14, "c=267"),

line(-2,-3,3.01144,-1.15579),
line(3.01144,-1.15579,0.15771,0.34858),
line(0.15771,0.34858,-2,-3),

locate(-2.28, -3.12, "A"),
locate(-1.28, -1.78, 37^o),
locate(1.3, 0.52, "a=???"),

locate(3.16, -1.12, "B"),
locate(1.58, -0.62 , 48^o),
locate(-1.05,-0.5 , "b"),

locate(-0.14,0.92, "C"),
locate(0.06,0.22, 95^o),

locate(-4.8,-6.3,matrix(1,5,"Diagram","is","not","to","scale"))
)
}}}


Use the law of sines to determine 'a'.
sin(A)/a = sin(C)/c
sin(37)/a = sin(95)/267
267*sin(37) = a*sin(95)
a*sin(95) = 267*sin(37)
a = 267*sin(37)/sin(95)
a = 161.298400292027
a = <font color=red>161.2984</font>
The shortest side is <font color=red>approximately 161.2984 meters</font> long.
Round this value however your teacher instructs.
Make sure your calculator is in degree mode.
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