Obtuse 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%

✖Obtuse Angle between Pair of Lines is the angle between any pair of lines which is greater than 90 degrees, in the two dimensional plane.ⓘ Obtuse Angle between Pair of Lines [∠_Obtuse]

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Obtuse Angle between Pair of Lines Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

Obtuse Angle between Pair of Lines - (Measured in Radian) - Obtuse Angle between Pair of Lines is the angle between any pair of lines which is greater 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

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

Evaluating ... ...

∠_Obtuse = 2.74680153389003

STEP 3: Convert Result to Output's Unit

2.74680153389003 Radian -->157.380135051989 Degree (Check conversion here)

FINAL ANSWER

157.380135051989 ≈ 157.3801 Degree <-- Obtuse Angle between Pair of Lines

(Calculation completed in 00.004 seconds)

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Credits

Created by Anirudh Singh

National Institute of Technology (NIT), Jamshedpur

Anirudh Singh has created this Calculator and 300+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

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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)))

Obtuse Angle between Pair of Lines Formula

LaTeX Go

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 Obtuse Angle between Pair of Lines?

Obtuse Angle between Pair of Lines calculator uses 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))) to calculate the Obtuse Angle between Pair of Lines, Obtuse Angle between Pair of Lines formula is defined as the angle between any pair of lines which is greater than 90 degrees, in the two dimensional plane. Obtuse Angle between Pair of Lines is denoted by ∠_Obtuse symbol.

How to calculate Obtuse Angle between Pair of Lines using this online calculator? To use this online calculator for Obtuse 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 Obtuse Angle between Pair of Lines calculation can be explained with given input values -> 9017.218 = pi-arctan(abs(((-0.2)-(0.2))/(1+(0.2)*(-0.2)))).

FAQ

What is Obtuse Angle between Pair of Lines?

Obtuse Angle between Pair of Lines formula is defined as the angle between any pair of lines which is greater than 90 degrees, in the two dimensional plane and is represented as ∠_Obtuse = pi-arctan(abs((m₂-(m₁))/(1+(m₁)*m₂))) or 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))). 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 Obtuse Angle between Pair of Lines?

Obtuse Angle between Pair of Lines formula is defined as the angle between any pair of lines which is greater than 90 degrees, in the two dimensional plane is calculated using 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))). To calculate Obtuse 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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