SOLUTION: what are the angle measures of △GHI in order from smallest to largest, given that HI=42 miles, GH=69 miles, and GI=82 miles.

Algebra ->  Triangles -> SOLUTION: what are the angle measures of △GHI in order from smallest to largest, given that HI=42 miles, GH=69 miles, and GI=82 miles.      Log On


   

Question 1151798: what are the angle measures of △GHI in order from smallest to largest, given that HI=42 miles, GH=69 miles, and GI=82 miles.
Found 2 solutions by MathLover1, jim_thompson5910:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the angle measures of △ GHI in order from smallest to largest,
given that"
HI=42 miles,=> shortest side is opposite the smallest angle which is < I
GH=69 miles, =>is opposite the angle < G
GI=82 miles => longest side is opposite the largest angle which is < H

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Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

HI = 42 ... smallest side
GH = 69
GI = 82 ... largest side

Smallest angle is opposite smallest side. Smallest angle is angle G.
Largest angle is opposite largest side. Largest angle is angle H.
Medium angle is opposite medium side. Medium angle is angle I.

@MathLover1 has the right idea, though the formulas should have the denominator inside the arccosine function. This is because c%5E2+=+a%5E2%2Bb%5E2+-+2%2Aa%2Ab%2Acos%28C%29 solves to C+=+arccos%28%28a%5E2%2Bb%5E2-c%5E2%29%2F%282%2Aa%2Ab%29%29 (law of cosines). Also, angle G and I should be swapped.

The three angle measures are approximately:
angle G = 30.79
angle I = 57.24
angle H = 91.97

Diagram: