Angle between two lines What is the size of the angle between the two lines 3x-2y+1=0 and x-3y=0 (answer in degrees and minutes) 15 degrees, 15 minutes a
62 degrees, 6 minutes b
43 degrees, 31 minutes c
37 degrees, 52 minutes d
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d) 37 degrees, 52 minutes

Step-by-step explanation:

3x-2y+1=0       y = 3/2 x + 1/2       ... slope₁ (m₁ = 3/2)

x-3y=0           3y =1/3 x                      ... slope₂ (m₂ = 1/3)

acute angle between two slopes: tan θ = (m₁-m₂) / (1+m₁*m₂)

tan θ = (3/2 - 1/3) / (1 + 3/2*1/3) = (7/6) / (3/2) = 7/9 = 0.77777777

θ = 37.875°

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,