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Question

Two sides of a triangle are 2 and 3 and the included angle is 30 then the in-radius r of the triangle is equal
 



Your Answer
A

14(31)

Your Answer
B

12(3+1)

Correct Answer
C

12(31)

Your Answer
D

14(3+1)


Solution

The correct option is C

12(31)


We know that r=(sa)tanA2.
Let the given sides be b and c and A=30 then

 a2=b2+c22bccosA by cosine rule =4+343cos30a2=743×22=76=1a2=1a=12s=a+b+c=1+2+3=3+32s2a=3+32(sa)=3+12A=30A2=15tanA2=tan15=313+1r=(sa)tanA2=3+12.313+1=12(31)

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