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

✖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 [S_Longer]			+10% -10%
✖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%
✖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.ⓘ Smaller Angle of Scalene Triangle [∠_Smaller]			+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 given Smaller Angle and other Sides [S_Shorter]

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
S_Shorter = sqrt(S_Longer^2+S_Medium^2-2*S_Longer*S_Medium*cos(∠_Smaller))
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

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.
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.
Smaller Angle of Scalene Triangle - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Longer Side of Scalene Triangle: 20 Meter --> 20 Meter No Conversion Required
Medium Side of Scalene Triangle: 14 Meter --> 14 Meter No Conversion Required
Smaller Angle of Scalene Triangle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_Shorter = sqrt(S_Longer^2+S_Medium^2-2*S_Longer*S_Medium*cos(∠_Smaller)) --> sqrt(20^2+14^2-2*20*14*cos(0.5235987755982))

Evaluating ... ...

S_Shorter = 10.5368768561047

STEP 3: Convert Result to Output's Unit

10.5368768561047 Meter --> No Conversion Required

FINAL ANSWER

10.5368768561047 ≈ 10.53688 Meter <-- Shorter Side of Scalene Triangle

(Calculation completed in 00.020 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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< Shorter Side of Scalene Triangle Calculators

Shorter Side of Scalene Triangle given Smaller Angle and other Sides

LaTeX Go 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))

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

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

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

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

Shorter Side of Scalene Triangle

LaTeX Go Shorter Side of Scalene Triangle = Perimeter of Scalene Triangle-(Longer Side of Scalene Triangle+Medium Side of Scalene Triangle)

< Sides 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))

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)

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

Shorter Side of Scalene Triangle given Smaller Angle and other Sides calculator 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 calculate 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 calculate Shorter Side of Scalene Triangle given Smaller Angle and other Sides using this online calculator? To use this online calculator 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. Here is how the Shorter Side of Scalene Triangle given Smaller Angle and other Sides calculation can be explained with given input values -> 10.53688 = sqrt(20^2+14^2-2*20*14*cos(0.5235987755982)).

FAQ

What is Shorter Side of Scalene Triangle given Smaller Angle and other Sides?

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 and is represented as S_Shorter = sqrt(S_Longer^2+S_Medium^2-2*S_Longer*S_Medium*cos(∠_Smaller)) or 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)). 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, The Medium Side of Scalene Triangle is the length of the second longer side out of the three sides & 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.

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

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 is calculated using 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 calculate Shorter Side of Scalene Triangle given Smaller Angle and other Sides, you need Longer Side of Scalene Triangle (S_Longer), Medium Side of Scalene Triangle (S_Medium) & Smaller Angle of Scalene Triangle (∠_Smaller). With our tool, you need to enter the respective value for Longer Side of Scalene Triangle, Medium Side of Scalene Triangle & Smaller 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 Shorter Side of Scalene Triangle?

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

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

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