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

GoShorter Side of Scalene Triangle given Smaller Angle, Larger Angle and Longer Side Formula

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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. Check FAQs

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

S_Shorter - Shorter Side of Scalene Triangle?S_Longer - Longer Side of Scalene Triangle?S_Medium - Medium Side of Scalene Triangle?∠_Smaller - Smaller Angle of Scalene Triangle?

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

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

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

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

10.5369 = \sqrt{20^{2} + 14^{2} - 2 \cdot 20 \cdot 14 \cdot \cos (30)}

10.5369m = \sqrt{{20m}^{2} + {14m}^{2} - 2 \cdot 20m \cdot 14m \cdot \cos (30°)}

10.5369 = \sqrt{20^{2} + 14^{2} - 2 \cdot 20 \cdot 14 \cdot \cos (30)}

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

S Shorter = \sqrt{{20m}^{2} + {14m}^{2} - 2 \cdot 20m \cdot 14m \cdot \cos (30°)}

Next Step Convert Units

∴

S Shorter = \sqrt{{20m}^{2} + {14m}^{2} - 2 \cdot 20m \cdot 14m \cdot \cos (0.5236rad)}

Next Step Prepare to Evaluate

∴

S Shorter = \sqrt{20^{2} + 14^{2} - 2 \cdot 20 \cdot 14 \cdot \cos (0.5236)}

Next Step Evaluate

∴

S Shorter = 10.5368768561047m

LAST Step Rounding Answer

∴

S Shorter = 10.5369m

Shorter Side of Scalene Triangle given Smaller Angle and other Sides Formula Elements

Variables

Functions

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

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

Smaller Angle of Scalene Triangle

The Smaller Angle of Scalene Triangle is the measure of the wideness of sides that join to form the corner opposite the shorter side of the Scalene Triangle.

Symbol: ∠_Smaller

Measurement: AngleUnit: °

Note: Value should be between 0 to 60.

Formulas to find Smaller 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 Shorter Side of Scalene Triangle

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

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

Other formulas in Shorter Side of Scalene Triangle category

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

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

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

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

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)}

How to Evaluate Shorter Side of Scalene Triangle given Smaller Angle and other Sides?

Shorter Side of Scalene Triangle given Smaller Angle and other Sides evaluator uses Shorter Side of Scalene Triangle = sqrt(Longer Side of Scalene Triangle^2+Medium Side of Scalene Triangle^2-2*Longer Side of Scalene Triangle*Medium Side of Scalene Triangle*cos(Smaller Angle of Scalene Triangle)) to evaluate the Shorter Side of Scalene Triangle, The Shorter Side of Scalene Triangle given Smaller Angle and other Sides formula is defined as the length of the side opposite to the smaller angle, calculated using the remaining two sides - longer side and medium side - and their inner angle, which is the smaller angle. Shorter Side of Scalene Triangle is denoted by S_Shorter symbol.

How to evaluate Shorter Side of Scalene Triangle given Smaller Angle and other Sides using this online evaluator? To use this online evaluator for Shorter Side of Scalene Triangle given Smaller Angle and other Sides, enter Longer Side of Scalene Triangle (S_Longer), Medium Side of Scalene Triangle (S_Medium) & Smaller Angle of Scalene Triangle (∠_Smaller) and hit the calculate button.

FAQs on Shorter Side of Scalene Triangle given Smaller Angle and other Sides

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

The formula of Shorter Side of Scalene Triangle given Smaller Angle and other Sides is expressed as Shorter Side of Scalene Triangle = sqrt(Longer Side of Scalene Triangle^2+Medium Side of Scalene Triangle^2-2*Longer Side of Scalene Triangle*Medium Side of Scalene Triangle*cos(Smaller Angle of Scalene Triangle)). Here is an example- 10.53688 = sqrt(20^2+14^2-2*20*14*cos(0.5235987755982)).

How to calculate Shorter Side of Scalene Triangle given Smaller Angle and other Sides?

With Longer Side of Scalene Triangle (S_Longer), Medium Side of Scalene Triangle (S_Medium) & Smaller Angle of Scalene Triangle (∠_Smaller) we can find Shorter Side of Scalene Triangle given Smaller Angle and other Sides using the formula - Shorter Side of Scalene Triangle = sqrt(Longer Side of Scalene Triangle^2+Medium Side of Scalene Triangle^2-2*Longer Side of Scalene Triangle*Medium Side of Scalene Triangle*cos(Smaller Angle of Scalene Triangle)). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

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

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

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

Can the Shorter Side of Scalene Triangle given Smaller Angle and other Sides be negative?

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

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

Shorter Side of Scalene Triangle given Smaller 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 Shorter Side of Scalene Triangle given Smaller Angle and other Sides can be measured.

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

​GoShorter Side of Scalene Triangle given Smaller Angle, Larger Angle and Longer Side Formula

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

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

Shorter Side of Scalene Triangle given Smaller Angle and other Sides Formula Elements

Other Formulas to find Shorter Side of Scalene Triangle

Other formulas in Shorter Side of Scalene Triangle category

How to Evaluate Shorter Side of Scalene Triangle given Smaller Angle and other Sides?

FAQs on Shorter Side of Scalene Triangle given Smaller Angle and other Sides

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GoShorter Side of Scalene Triangle given Smaller Angle, Larger Angle and Longer Side Formula