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Acute Angle between Pair of Lines Formula

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Acute Angle between Pair of Lines is the angle between any pair of lines which is less than 90 degrees, in the two dimensional plane. Check FAQs

∠ Acute = \arctan (| \frac{m 2 - (m 1)}{1 + (m 1) \cdot m 2} |)

∠_Acute - Acute Angle between Pair of Lines?m₂ - Slope of Second Line?m₁ - Slope of First Line?

Acute Angle between Pair of Lines Example

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Here is how the Acute Angle between Pair of Lines equation looks like with Values.

Here is how the Acute Angle between Pair of Lines equation looks like with Units.

Here is how the Acute Angle between Pair of Lines equation looks like.

22.6199 = \arctan (| \frac{-0.2 - (0.2)}{1 + (0.2) \cdot -0.2} |)

22.6199° = \arctan (| \frac{-0.2 - (0.2)}{1 + (0.2) \cdot -0.2} |)

22.6199 = \arctan (| \frac{-0.2 - (0.2)}{1 + (0.2) \cdot -0.2} |)

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Acute Angle between Pair of Lines Solution

Follow our step by step solution on how to calculate Acute Angle between Pair of Lines?

FIRST Step Consider the formula

∠ Acute = \arctan (| \frac{m 2 - (m 1)}{1 + (m 1) \cdot m 2} |)

Next Step Substitute values of Variables

∴

∠ Acute = \arctan (| \frac{-0.2 - (0.2)}{1 + (0.2) \cdot -0.2} |)

Next Step Prepare to Evaluate

∴

∠ Acute = \arctan (| \frac{-0.2 - (0.2)}{1 + (0.2) \cdot -0.2} |)

Next Step Evaluate

∴

∠ Acute = 0.394791119699762rad

Next Step Convert to Output's Unit

∴

∠ Acute = 22.6198649480447°

LAST Step Rounding Answer

∴

∠ Acute = 22.6199°

Acute Angle between Pair of Lines Formula Elements

Variables

Functions

Acute Angle between Pair of Lines

Acute Angle between Pair of Lines is the angle between any pair of lines which is less than 90 degrees, in the two dimensional plane.

Symbol: ∠_Acute

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Acute Angle between Pair of Lines

Slope of Second Line

Slope of Second Line is the ratio of differences of y coordinates to x coordinates of any two points on the second line in a specific order.

Symbol: m₂

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Slope of Second Line

Slope of First Line

Slope of First Line is the ratio of differences of y coordinates to x coordinates of any two points on the first line in a specific order.

Symbol: m₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Slope of First Line

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

ctan

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: ctan(Angle)

arctan

Inverse trigonometric functions are usually accompanied by the prefix - arc. Mathematically, we represent arctan or the inverse tangent function as tan-1 x or arctan(x).

Syntax: arctan(Number)

abs

The absolute value of a number is its distance from zero on the number line. It's always a positive value, as it represents the magnitude of a number without considering its direction.

Syntax: abs(Number)

Other formulas in Pair of Lines category

Go Obtuse Angle between Pair of Lines

∠ Obtuse = π - \arctan (| \frac{m 2 - (m 1)}{1 + (m 1) \cdot m 2} |)

Go Shortest Distance between Parallel Lines

d Parallel Lines = mod \underset{̲}{u} s \frac{c 1 - (c 2)}{\sqrt{({L x}^{2}) + ({L y}^{2})}}

How to Evaluate Acute Angle between Pair of Lines?

Acute Angle between Pair of Lines evaluator uses Acute Angle between Pair of Lines = arctan(abs((Slope of Second Line-(Slope of First Line))/(1+(Slope of First Line)*Slope of Second Line))) to evaluate the Acute Angle between Pair of Lines, Acute Angle between Pair of Lines formula is defined as the angle between any pair of lines which is less than 90 degrees, in the two dimensional plane. Acute Angle between Pair of Lines is denoted by ∠_Acute symbol.

How to evaluate Acute Angle between Pair of Lines using this online evaluator? To use this online evaluator for Acute Angle between Pair of Lines, enter Slope of Second Line (m₂) & Slope of First Line (m₁) and hit the calculate button.

FAQs on Acute Angle between Pair of Lines

What is the formula to find Acute Angle between Pair of Lines?

The formula of Acute Angle between Pair of Lines is expressed as Acute Angle between Pair of Lines = arctan(abs((Slope of Second Line-(Slope of First Line))/(1+(Slope of First Line)*Slope of Second Line))). Here is an example- 1296.023 = arctan(abs(((-0.2)-(0.2))/(1+(0.2)*(-0.2)))).

How to calculate Acute Angle between Pair of Lines?

With Slope of Second Line (m₂) & Slope of First Line (m₁) we can find Acute Angle between Pair of Lines using the formula - Acute Angle between Pair of Lines = arctan(abs((Slope of Second Line-(Slope of First Line))/(1+(Slope of First Line)*Slope of Second Line))). This formula also uses TangentCotangent CotangentInverse Tangent, Absolute function(s).

Can the Acute Angle between Pair of Lines be negative?

No, the Acute Angle between Pair of Lines, measured in Angle cannot be negative.

Which unit is used to measure Acute Angle between Pair of Lines?

Acute Angle between Pair of Lines is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Acute Angle between Pair of Lines can be measured.

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