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

GoLonger Side of Scalene Triangle given Larger Angle, Medium Angle and Medium Side Formula

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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. Check FAQs

S Longer = \sqrt{{S Medium}^{2} + {S Shorter}^{2} - 2 \cdot S Medium \cdot S Shorter \cdot \cos (∠ Larger)}

S_Longer - Longer Side of Scalene Triangle?S_Medium - Medium Side of Scalene Triangle?S_Shorter - Shorter Side of Scalene Triangle?∠_Larger - Larger Angle of Scalene Triangle?

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

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Here is how the Longer Side of Scalene Triangle given Larger Angle and other Sides equation looks like with Values.

Here is how the Longer Side of Scalene Triangle given Larger Angle and other Sides equation looks like with Units.

Here is how the Longer Side of Scalene Triangle given Larger Angle and other Sides equation looks like.

19.7931 = \sqrt{14^{2} + 10^{2} - 2 \cdot 14 \cdot 10 \cdot \cos (110)}

19.7931m = \sqrt{{14m}^{2} + {10m}^{2} - 2 \cdot 14m \cdot 10m \cdot \cos (110°)}

19.7931 = \sqrt{14^{2} + 10^{2} - 2 \cdot 14 \cdot 10 \cdot \cos (110)}

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

Follow our step by step solution on how to calculate Longer Side of Scalene Triangle given Larger Angle and other Sides?

FIRST Step Consider the formula

S Longer = \sqrt{{S Medium}^{2} + {S Shorter}^{2} - 2 \cdot S Medium \cdot S Shorter \cdot \cos (∠ Larger)}

Next Step Substitute values of Variables

∴

S Longer = \sqrt{{14m}^{2} + {10m}^{2} - 2 \cdot 14m \cdot 10m \cdot \cos (110°)}

Next Step Convert Units

∴

S Longer = \sqrt{{14m}^{2} + {10m}^{2} - 2 \cdot 14m \cdot 10m \cdot \cos (1.9199rad)}

Next Step Prepare to Evaluate

∴

S Longer = \sqrt{14^{2} + 10^{2} - 2 \cdot 14 \cdot 10 \cdot \cos (1.9199)}

Next Step Evaluate

∴

S Longer = 19.7930705079099m

LAST Step Rounding Answer

∴

S Longer = 19.7931m

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

Variables

Functions

Longer Side of Scalene Triangle

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.

Symbol: S_Longer

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Longer Side of Scalene Triangle

Medium Side of Scalene Triangle

The Medium Side of Scalene Triangle is the length of the second longer side out of the three sides.

Symbol: S_Medium

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Medium Side of Scalene Triangle

Shorter Side of Scalene Triangle

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.

Symbol: S_Shorter

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Shorter Side of Scalene Triangle

Larger Angle of Scalene Triangle

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.

Symbol: ∠_Larger

Measurement: AngleUnit: °

Note: Value should be between 60 to 180.

Formulas to find Larger Angle of Scalene Triangle

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: sqrt(Number)

Other Formulas to find Longer Side of Scalene Triangle

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

S Longer = S Medium \cdot \frac{\sin (∠ Larger)}{\sin (∠ Medium)}

Other formulas in Longer Side of Scalene Triangle category

Go Medium Side of Scalene Triangle given Medium Angle and other Sides

S Medium = \sqrt{{S Longer}^{2} + {S Shorter}^{2} - 2 \cdot S Longer \cdot S Shorter \cdot \cos (∠ Medium)}

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

S Medium = S Shorter \cdot \frac{\sin (∠ Medium)}{\sin (∠ Smaller)}

Go Shorter Side of Scalene Triangle given Smaller Angle and other Sides

S Shorter = \sqrt{{S Longer}^{2} + {S Medium}^{2} - 2 \cdot S Longer \cdot S Medium \cdot \cos (∠ Smaller)}

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

S Shorter = S Longer \cdot \frac{\sin (∠ Smaller)}{\sin (∠ Larger)}

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

Longer Side of Scalene Triangle given Larger Angle and other Sides evaluator 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 evaluate 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 evaluate Longer Side of Scalene Triangle given Larger Angle and other Sides using this online evaluator? To use this online evaluator 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.

FAQs on Longer Side of Scalene Triangle given Larger Angle and other Sides

What is the formula to find Longer Side of Scalene Triangle given Larger Angle and other Sides?

The formula of Longer Side of Scalene Triangle given Larger Angle and other Sides is expressed as 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)). Here is an example- 19.79307 = sqrt(14^2+10^2-2*14*10*cos(1.9198621771934)).

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

With Medium Side of Scalene Triangle (S_Medium), Shorter Side of Scalene Triangle (S_Shorter) & Larger Angle of Scalene Triangle (∠_Larger) we can find Longer Side of Scalene Triangle given Larger Angle and other Sides using the formula - 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)). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Longer Side of Scalene Triangle?

Here are the different ways to Calculate Longer Side of Scalene Triangle-

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

Can the Longer Side of Scalene Triangle given Larger Angle and other Sides be negative?

No, the Longer Side of Scalene Triangle given Larger Angle and other Sides, measured in Length cannot be negative.

Which unit is used to measure Longer Side of Scalene Triangle given Larger Angle and other Sides?

Longer Side of Scalene Triangle given Larger Angle and other Sides is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Longer Side of Scalene Triangle given Larger Angle and other Sides can be measured.

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

​GoLonger Side of Scalene Triangle given Larger Angle, Medium Angle and Medium Side Formula

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

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

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

Other Formulas to find Longer Side of Scalene Triangle

Other formulas in Longer Side of Scalene Triangle category

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

FAQs on Longer Side of Scalene Triangle given Larger Angle and other Sides

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GoLonger Side of Scalene Triangle given Larger Angle, Medium Angle and Medium Side Formula