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question mark

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

Yogita Sri Alekya , 7 Years ago
Grade 11
anser 2 Answers
Ravi malvia

Last Activity: 7 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

Last Activity: 3 Years ago

Given, sinAsinB= 
c 
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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