Answer:
The measure of the acute angle is 18.4°
Step-by-step explanation:
The angle between a line of equation y = m x + b and the positive part of the x-axis is Ф = [tex]tan^{-1}[/tex](m), which means tan Ф = m, where m is the slope of the line
Let us use this rule to solve the question
∵ A line of equation y = [tex]\frac{1}{3}[/tex] x + 4 makes with a horizontal line an acute ∠
→ Compare the equation of the line by the form of the equation above
∴ m = [tex]\frac{1}{3}[/tex]
→ Assume that the acute angle is Ф
∴ The acute angle between the line and the horizontal line is Ф
→ By using the rule above
∵ tan Ф = m
∴ tan Ф = [tex]\frac{1}{3}[/tex]
→ Use [tex]tan^{-1}[/tex] to find Ф
∵ Ф = [tex]tan^{-1}[/tex] ( [tex]\frac{1}{3}[/tex] )
∴ Ф = 18.43494882
→ Round it to the nearest tenth
∴ Ф = 18.4°
∴ The measure of the acute angle is 18.4°
