Question

Find the measure of the acute angle that line y=1/3x+4 makes with a horizontal line. Round your answer to the nearest tenth.

Also, I hope you are having a good day.

Answer 1

The measure of the acute angle is 18.4°

Explanation:

The angle between a line of equation y = m x + b and the positive part of the x-axis is Ф =
`tan^(-1)`(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 =
`(1)/(3)` x + 4 makes with a horizontal line an acute ∠

→ Compare the equation of the line by the form of the equation above

∴ m =
`(1)/(3)`

→ 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 =
`(1)/(3)`

→ Use
`tan^(-1)` to find Ф

∵ Ф =
`tan^(-1)` (
`(1)/(3)` )

∴ Ф = 18.43494882

→ Round it to the nearest tenth

∴ Ф = 18.4°

∴ The measure of the acute angle is 18.4°