Acute Angle between Pair of Lines Calculator

✖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.ⓘ Slope of Second Line [m₂]			+10% -10%
✖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.ⓘ Slope of First Line [m₁]			+10% -10%

✖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.ⓘ Acute Angle between Pair of Lines [∠_Acute]

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Acute Angle between Pair of Lines Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
∠_Acute = arctan(abs((m₂-(m₁))/(1+(m₁)*m₂)))
This formula uses 4 Functions, 3 Variables

Functions Used

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., 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., 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)., 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., abs(Number)

Variables Used

Acute Angle between Pair of Lines - (Measured in Radian) - 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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Slope of Second Line: -0.2 --> No Conversion Required
Slope of First Line: 0.2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_Acute = arctan(abs((m₂-(m₁))/(1+(m₁)*m₂))) --> arctan(abs(((-0.2)-(0.2))/(1+(0.2)*(-0.2))))

Evaluating ... ...

∠_Acute = 0.394791119699762

STEP 3: Convert Result to Output's Unit

0.394791119699762 Radian -->22.6198649480447 Degree (Check conversion here)

FINAL ANSWER

22.6198649480447 ≈ 22.61986 Degree <-- Acute Angle between Pair of Lines

(Calculation completed in 00.004 seconds)

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Credits

Created by Venkata Sai Prasanna Aradhyula

Birla Institute of Technology & Science (BITS), Hyderabad

Venkata Sai Prasanna Aradhyula has created this Calculator and 10+ more calculators!

Verified by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< Pair of Lines Calculators

Obtuse Angle between Pair of Lines

LaTeX Go Obtuse Angle between Pair of Lines = pi-arctan(abs((Slope of Second Line-(Slope of First Line))/(1+(Slope of First Line)*Slope of Second Line)))

Shortest Distance between Parallel Lines

LaTeX Go Shortest Distance of Parallel Lines = modulus(Constant Term of First Line-(Constant Term of Second Line))/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2))

Acute Angle between Pair of Lines

LaTeX Go 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)))

Acute Angle between Pair of Lines Formula

LaTeX Go

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)))
∠_Acute = arctan(abs((m₂-(m₁))/(1+(m₁)*m₂)))

What is a Line?

A Line in two dimensional plane is the infinite extension of the line segment joining two arbitrary points, in both directions. In a Line for any two arbitrary points, the ratio of difference of y coordinates to the difference of x coordinates in a specific order is a constant value. That value is called the slope of that Line. Every Line has a slope, which can be any real number - positive or negative or zero.

How to Calculate Acute Angle between Pair of Lines?

Acute Angle between Pair of Lines calculator 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 calculate 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 calculate Acute Angle between Pair of Lines using this online calculator? To use this online calculator for Acute Angle between Pair of Lines, enter Slope of Second Line (m₂) & Slope of First Line (m₁) and hit the calculate button. Here is how the Acute Angle between Pair of Lines calculation can be explained with given input values -> 1296.023 = arctan(abs(((-0.2)-(0.2))/(1+(0.2)*(-0.2)))).

FAQ

What is 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 and is represented as ∠_Acute = arctan(abs((m₂-(m₁))/(1+(m₁)*m₂))) or 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))). 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 & 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.

How to calculate 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 is calculated using 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 calculate Acute Angle between Pair of Lines, you need Slope of Second Line (m₂) & Slope of First Line (m₁). With our tool, you need to enter the respective value for Slope of Second Line & Slope of First Line and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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