Longer Side of Scalene Triangle given Larger Angle and other Sides Calculator

✖The Medium Side of Scalene Triangle is the length of the second longer side out of the three sides.ⓘ Medium Side of Scalene Triangle [S_Medium]			+10% -10%
✖Shorter Side of Scalene Triangle is the length of the shorter side out of the three sides. In other words, shorter side of the Scalene Triangle is the side opposite to the smaller angle.ⓘ Shorter Side of Scalene Triangle [S_Shorter]			+10% -10%
✖Larger Angle of Scalene Triangle is the measure of wideness of sides which join to form the corner which is opposite to the longer side of the Scalene Triangle.ⓘ Larger Angle of Scalene Triangle [∠_Larger]			+10% -10%

✖The Longer Side of Scalene Triangle is the length of the longer side out of the three sides. In other words, the longer side of the Scalene Triangle is the side opposite to the larger angle.ⓘ Longer Side of Scalene Triangle given Larger Angle and other Sides [S_Longer]

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Longer Side of Scalene Triangle given Larger Angle and other Sides Solution

STEP 0: Pre-Calculation Summary

Formula Used

Longer Side of Scalene Triangle = sqrt(Medium Side of Scalene Triangle^2+Shorter Side of Scalene Triangle^2-2*Medium Side of Scalene Triangle*Shorter Side of Scalene Triangle*cos(Larger Angle of Scalene Triangle))
S_Longer = sqrt(S_Medium^2+S_Shorter^2-2*S_Medium*S_Shorter*cos(∠_Larger))
This formula uses 2 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Longer Side of Scalene Triangle - (Measured in Meter) - The Longer Side of Scalene Triangle is the length of the longer side out of the three sides. In other words, the longer side of the Scalene Triangle is the side opposite to the larger angle.
Medium Side of Scalene Triangle - (Measured in Meter) - The Medium Side of Scalene Triangle is the length of the second longer side out of the three sides.
Shorter Side of Scalene Triangle - (Measured in Meter) - Shorter Side of Scalene Triangle is the length of the shorter side out of the three sides. In other words, shorter side of the Scalene Triangle is the side opposite to the smaller angle.
Larger Angle of Scalene Triangle - (Measured in Radian) - Larger Angle of Scalene Triangle is the measure of wideness of sides which join to form the corner which is opposite to the longer side of the Scalene Triangle.

STEP 1: Convert Input(s) to Base Unit

Medium Side of Scalene Triangle: 14 Meter --> 14 Meter No Conversion Required
Shorter Side of Scalene Triangle: 10 Meter --> 10 Meter No Conversion Required
Larger Angle of Scalene Triangle: 110 Degree --> 1.9198621771934 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_Longer = sqrt(S_Medium^2+S_Shorter^2-2*S_Medium*S_Shorter*cos(∠_Larger)) --> sqrt(14^2+10^2-2*14*10*cos(1.9198621771934))

Evaluating ... ...

S_Longer = 19.7930705079099

STEP 3: Convert Result to Output's Unit

19.7930705079099 Meter --> No Conversion Required

FINAL ANSWER

19.7930705079099 ≈ 19.79307 Meter <-- Longer Side of Scalene Triangle

(Calculation completed in 00.008 seconds)

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Created by Jaseem K

IIT Madras (IIT Madras), Chennai

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Verified by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< Longer Side of Scalene Triangle Calculators

Longer Side of Scalene Triangle given Larger Angle and other Sides

LaTeX Go Longer Side of Scalene Triangle = sqrt(Medium Side of Scalene Triangle^2+Shorter Side of Scalene Triangle^2-2*Medium Side of Scalene Triangle*Shorter Side of Scalene Triangle*cos(Larger Angle of Scalene Triangle))

Longer Side of Scalene Triangle given Larger Angle, Smaller Angle and Shorter Side

LaTeX Go Longer Side of Scalene Triangle = Shorter Side of Scalene Triangle*sin(Larger Angle of Scalene Triangle)/sin(Smaller Angle of Scalene Triangle)

Longer Side of Scalene Triangle given Larger Angle, Medium Angle and Medium Side

LaTeX Go Longer Side of Scalene Triangle = Medium Side of Scalene Triangle*sin(Larger Angle of Scalene Triangle)/sin(Medium Angle of Scalene Triangle)

Longer Side of Scalene Triangle given Semi Perimeter and other Sides

LaTeX Go Longer Side of Scalene Triangle = 2*Semiperimeter of Scalene Triangle-(Medium Side of Scalene Triangle+Shorter Side of Scalene Triangle)

< Sides of Scalene Triangle Calculators

Longer Side of Scalene Triangle given Larger Angle and other Sides

Medium Side of Scalene Triangle given Medium Angle and other Sides

LaTeX Go Medium Side of Scalene Triangle = sqrt(Longer Side of Scalene Triangle^2+Shorter Side of Scalene Triangle^2-2*Longer Side of Scalene Triangle*Shorter Side of Scalene Triangle*cos(Medium Angle of Scalene Triangle))

Medium Side of Scalene Triangle given Medium Angle, Smaller Angle and Shorter Side

LaTeX Go Medium Side of Scalene Triangle = Shorter Side of Scalene Triangle*sin(Medium Angle of Scalene Triangle)/sin(Smaller Angle of Scalene Triangle)

Longer Side of Scalene Triangle given Larger Angle, Medium Angle and Medium Side

LaTeX Go Longer Side of Scalene Triangle = Medium Side of Scalene Triangle*sin(Larger Angle of Scalene Triangle)/sin(Medium Angle of Scalene Triangle)

Longer Side of Scalene Triangle given Larger Angle and other Sides Formula

LaTeX Go

What is a Scalene Triangle ?

A triangle with all sides are distinct in length is called a Scalene Triangle. Mainly triangles are classified into three on the basis of side lengths. If all sides are equal in length then it is called Equilateral Triangle. If only two sides are equal in length then it is called Isosceles Triangle. If no sides are equal, or all sides are distinct in length then it is called Scalene Triangle. Cases are similar in terms of angles also. That is, Equilateral Triangles have all three angles equal. Isosceles Triangles have atleast two angles are equal. And then, Scalene Triangles have all three angles are distinct.

Standard notations

Let a triangle is named as ABC. Then A, B and C represent respective angles of the triangle. They are usually called angle A, angle B and angle C respectively. The sides opposite to angles A, B and C are respectively called side a, side b and side c.

How to Calculate Longer Side of Scalene Triangle given Larger Angle and other Sides?

Longer Side of Scalene Triangle given Larger Angle and other Sides calculator uses Longer Side of Scalene Triangle = sqrt(Medium Side of Scalene Triangle^2+Shorter Side of Scalene Triangle^2-2*Medium Side of Scalene Triangle*Shorter Side of Scalene Triangle*cos(Larger Angle of Scalene Triangle)) to calculate the Longer Side of Scalene Triangle, The Longer Side of Scalene Triangle given Larger Angle and other Sides formula is defined as the length of the side opposite to the larger angle, calculated using its medium side and shorter side - and their inner angle, which is the larger angle. Longer Side of Scalene Triangle is denoted by S_Longer symbol.

How to calculate Longer Side of Scalene Triangle given Larger Angle and other Sides using this online calculator? To use this online calculator for Longer Side of Scalene Triangle given Larger Angle and other Sides, enter Medium Side of Scalene Triangle (S_Medium), Shorter Side of Scalene Triangle (S_Shorter) & Larger Angle of Scalene Triangle (∠_Larger) and hit the calculate button. Here is how the Longer Side of Scalene Triangle given Larger Angle and other Sides calculation can be explained with given input values -> 19.79307 = sqrt(14^2+10^2-2*14*10*cos(1.9198621771934)).

FAQ

What is Longer Side of Scalene Triangle given Larger Angle and other Sides?

The Longer Side of Scalene Triangle given Larger Angle and other Sides formula is defined as the length of the side opposite to the larger angle, calculated using its medium side and shorter side - and their inner angle, which is the larger angle and is represented as S_Longer = sqrt(S_Medium^2+S_Shorter^2-2*S_Medium*S_Shorter*cos(∠_Larger)) or Longer Side of Scalene Triangle = sqrt(Medium Side of Scalene Triangle^2+Shorter Side of Scalene Triangle^2-2*Medium Side of Scalene Triangle*Shorter Side of Scalene Triangle*cos(Larger Angle of Scalene Triangle)). The Medium Side of Scalene Triangle is the length of the second longer side out of the three sides, Shorter Side of Scalene Triangle is the length of the shorter side out of the three sides. In other words, shorter side of the Scalene Triangle is the side opposite to the smaller angle & Larger Angle of Scalene Triangle is the measure of wideness of sides which join to form the corner which is opposite to the longer side of the Scalene Triangle.

How to calculate Longer Side of Scalene Triangle given Larger Angle and other Sides?

The Longer Side of Scalene Triangle given Larger Angle and other Sides formula is defined as the length of the side opposite to the larger angle, calculated using its medium side and shorter side - and their inner angle, which is the larger angle is calculated using Longer Side of Scalene Triangle = sqrt(Medium Side of Scalene Triangle^2+Shorter Side of Scalene Triangle^2-2*Medium Side of Scalene Triangle*Shorter Side of Scalene Triangle*cos(Larger Angle of Scalene Triangle)). To calculate Longer Side of Scalene Triangle given Larger Angle and other Sides, you need Medium Side of Scalene Triangle (S_Medium), Shorter Side of Scalene Triangle (S_Shorter) & Larger Angle of Scalene Triangle (∠_Larger). With our tool, you need to enter the respective value for Medium Side of Scalene Triangle, Shorter Side of Scalene Triangle & Larger Angle of Scalene Triangle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Longer Side of Scalene Triangle?

In this formula, Longer Side of Scalene Triangle uses Medium Side of Scalene Triangle, Shorter Side of Scalene Triangle & Larger Angle of Scalene Triangle. We can use 3 other way(s) to calculate the same, which is/are as follows -

Longer Side of Scalene Triangle = Medium Side of Scalene Triangle*sin(Larger Angle of Scalene Triangle)/sin(Medium Angle of Scalene Triangle)
Longer Side of Scalene Triangle = Shorter Side of Scalene Triangle*sin(Larger Angle of Scalene Triangle)/sin(Smaller Angle of Scalene Triangle)
Longer Side of Scalene Triangle = 2*Semiperimeter of Scalene Triangle-(Medium Side of Scalene Triangle+Shorter Side of Scalene Triangle)

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