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 Consider circle H with a 5 centimeter radius. If the length of major arc RST is 25/3π, what is the measure of ∠RST?

 Feb 20, 2019
 #1
avatar+194 
+1

Given the major arc and the minor arc share the same chord, the angle RST will be:
∠RST=1/2∠RHT
∠RHT=1/3π=1/3×180=60
hence
∠RST=1/2×60=30°

 Answer: 30°
 

 Feb 20, 2019
 #3
avatar+102995 
+2

Nice, bigbrotheprodude.....!!!!

 

 

cool cool cool

CPhill  Feb 21, 2019
 #2
avatar+102995 
+3

The circumference of the circle will be     2pi (5) = 10 pi cm

 

So the measure of arc RST can be found as

 

(25/3) pi /  [10 pi  ]  = arc RST / 360

 

25/30 = arc RST / 360

 

5/6  = arc RST /360

 

(5/6)360 = arc RST

 

300° = arc RST

 

Then minor arc RT = 60°

 

And since angle RST is an inscribed angle intercepting minor arc RT, its measure is (1/2) 60° = 30°

 

Just as bigbrotheprodude  found....!!!!

 

 

cool cool  cool

 Feb 21, 2019

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