Question

the measure of the acute angle between line root 3 x minus 5 minus 2 is equal to zero and x minus root 3 Y + 1 is equal to zero is​

Answer 1

Step-by-step explanation:

The given lines are

3 x+y=1 and x+

3y=1⇒y=− 3

x+1 and y=− 31 x+ 31

Thus slope of line (1) is m

1 =− 3

while the slope of line (2) is m

2 =− 31

The acute angle i.e;θ between the two lines is given by

tanθ=

1+m

1 m2m 1 −m2

∣∣∣∣= ∣∣∣∣∣∣

−1+(− 3)

(−31)3+31

∣∣∣∣∣∣= ∣∣∣∣

1+13−3+1

∣∣∣∣∣∣

= 23−2

∣∣∣∣∣

⇒tanθ= 31 ,θ=30∘

Thus, the angle between the given lines is either

30 or 180∘ −30∘ =150∘