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.

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) (Show Source): You can put this solution on YOUR website!
the angle measures of △ in order from smallest to largest,
given that"
miles,=> shortest side is opposite the smallest angle which is <
miles, =>is opposite the angle <
miles => longest side is opposite the largest angle which is <

°
°
°
Answer by jim_thompson5910(35256) (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 solves to (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:

RELATED QUESTIONS
list the angles of triangle GHI in order from least to greatest measure if side GI is 7,... (answered by stanbon)
In triangle GHI, we have GH = HI = 25 and GI = 30. What is sin (answered by Fombitz)
A triangle has angle measures of 2x+10, 4x and 5x+5. What are the measures of each angle... (answered by nycsharkman)
When the measures of the angles of a triangle are placed in order, the difference between (answered by josgarithmetic,MathTherapy)
isosceles ghi has gh congruent to gi. gh is x^2, gi is -2x plus 15 and hi is -x plus 4... (answered by greenestamps)
Suppose you are given the coordinates of the vertices of TRIANGLE GHI. Which of the... (answered by jim_thompson5910)
1. What additional information do you need to prove triangle GHI is congruent to... (answered by KMST)
How do I prove congruence of these 2 triangles in a 2 column proof. I am given a picture... (answered by rothauserc)
the measure of the largest angle of a triangle is 45 degrees moe than the measure of the... (answered by checkley77)