If, sinA:sinB:sinC=3:4:5, then cosA:cosB is equal to
4:3
5:3
3:4
3:5
Explanation for the correct option.
Step 1: Find the length of the sides
Given that, sinA:sinB:sinC=3:4:5
Let, sinA=3x,sinB=4x,sinC=5x
Using sine rule i.e; asinA=bsinB=csinC we have:
a3x=b4x=c5x=kconstant
⇒a=3xk,b=4xk,c=5xk
Step 2: Find cosA:cosB
To find this we use the cosine rule i.e; cosA=b2+c2-a22bc.
cosA=4xk2+5xk2-3xk224xk5xk=16x2k2+25x2k2-9x2k240x2k2=32x2k240x2k2=45
Similarly for cosB.
cosB=3xk2+5xk2-4xk223xk5xk=15x2k2+25x2k2-16x2k230x2k2=18x2k240x2k2=35
So, cosA:cosB=45:35=4:3
Hence, option A is correct.