SOLUTION: The longest side of a triangle measured 267m,if two angles are 37and 48,find the shortest side of the triangle

Algebra ->  Triangles -> SOLUTION: The longest side of a triangle measured 267m,if two angles are 37and 48,find the shortest side of the triangle       Log On


   

Question 1200660: The longest side of a triangle measured 267m,if two angles are 37and 48,find the shortest side of the triangle
Found 2 solutions by Edwin McCravy, math_tutor2020:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
To find out which is the longest side, we use the fact that 
the longest side is opposite the largest angle.  Two of the 
angles are given as 37o and 48o, so the third angle is 
180o-(37o+48o) = 180o-85o = 95o.  
So the longest side is opposite the 95o angle.  We want to 
find the shortest side.  We use the fact that the shortest 
side is opposite the smallest angle.   So it's the side 
opposite the 37o-angle, which we will call x. Here is how 
the triangle looks, drawn approximately to scale:

  

We use the law of sines

267%2Fsin%2895%5Eo%29%22%22=%22%22x%2Fsin%2837%5Eo%29

Cross-multiply:

x%2Asin%2895%5Eo%29%22%22=%22%22267%2Asin%2837%5Eo%29

x%22%22=%22%22267%2Asin%2837%5Eo%29%2Fsin%2895%5Eo%29

x%22%22=%22%22267%2A0.6018150232%2F0.9961946981

x%22%22=%22%22161.2984003

Since the given side is rounded to 3 significant digits,
we round that to 161m.  

Edwin

Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: 161.2984 meters (approximate)

====================================================================================

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


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 = 161.2984
The shortest side is approximately 161.2984 meters long.
Round this value however your teacher instructs.
Make sure your calculator is in degree mode.