SOLUTION: Hi! I was wondering if you have a triangle on the shpere what is the range of values for the sum of the angles of a triangle on a sphere? I have seen this question posted before bu

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Question 724659: Hi! I was wondering if you have a triangle on the shpere what is the range of values for the sum of the angles of a triangle on a sphere? I have seen this question posted before but I didn't understand it. Could you explain how you got the answer too. Thanks:)
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Hi! I was wondering if you have a triangle on the shpere what is the range of values for the sum of the angles of a triangle on a sphere? I have seen this question posted before but I didn't understand it. Could you explain how you got the answer too.
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180 degrees < sum of angles < 360 degrees
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Draw a couple of pictures on a sphere.
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# 1
Draw a base on the equator.
Draw two sides that terminate in the north pole.
Notice that the 2 base angles are both 90 degrees
The vertex angle may be small but it is not zero.
So the sum of the angles is greater than 180 degrees.
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#2
Draw a base on the equator.
Draw two sides that are as far from one another
as possible but do not form a semi-circle.
The 2 base angles are both 90 degrees.
The vertex angle is large but cannot be 180 degrees.
So the sum of the angles is less than 2*90+180 = 360 degrees.
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Cheers,
Stan H.
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