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In triangle ABC ,SinA.SinB=ab/c square , then C = ??

In triangle ABC ,SinA.SinB=ab/c square , then C = ??

Grade:11

2 Answers

Ravi malvia
37 Points
3 years ago
sinA.sinB = ab/c2
\tiny \because a=2RsinA , b=2Rsinb, c=2Rsinc 
put them in equation 
   sinA.sinB = (2RsinA.2RsinB)/(2RsinC)2
now remaining equation is below_
  sin2C = 1
  sinC = \tiny \pm1   \tiny \Leftrightarrow  C = 90 degree or  -270 degree
Raj Prajapati
13 Points
3 months ago
Given, sinAsinB= 
2
 
ab
 
⇒c 
2
 = 
sinAsinB
ab
 =( 
sinA
a
 )( 
sinB
b
 )
⇒c 
2
 =( 
sinC
c
 ) 
2
 (∵ 
sinA
a
 = 
sinB
b
 = 
sinC
c
 )
⇒sin 
2
 C=1
⇒C=90 
 
Hence, ΔABC is a right angled triangle.

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