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97.

The angle θ between the lines having slope m1 and m2 is given by

tan θ = (m2−m1)/(1+m1*m2)

y=x -> slope m1=1
y=sqrt(3)x-> slope m2=sqrt(3)

tan θ = (sqrt(3)-1)/(1+1*sqrt(3))

tan θ = (sqrt(3)-1)/(1+sqrt(3)) ......rationalize

tan θ = 2 - sqrt(3)

θ =tan^-1(2 - sqrt(3))

θ =π/12 (result in radians)

θ =15°

[QUOTE="MathLover1, post: 1099548, member: 280"] 97. The angle θ between the lines having slope m1 and m2 is given by tan θ = (m2−m1)/(1+m1*m2) y=x -> slope [B]m1=1[/B] y=sqrt(3)x-> slope m2=[B]sqrt(3)[/B] tan θ =[B] [/B](sqrt(3)-1)/(1+1*sqrt(3))[B] [/B] tan θ = (sqrt(3)-1)/(1+sqrt(3)) ......rationalize tan θ = 2 - sqrt(3) θ =tan^-1(2 - sqrt(3)) [B]θ =π/12[/B] (result in radians) [B]θ =15° [IMG]https://www6b3.wolframalpha.com/Calculate/MSP/MSP37831c3bhadh551e5f4d000048eg1h2157c8b48f?MSPStoreType=image/gif&s=7[/IMG][/B] [/QUOTE]