Side A of Triangle Calculator

✖The Side B of Triangle is the length of the side B of the three sides. In other words, the side Bof the Triangle is the side opposite to the angle B.ⓘ Side B of Triangle [S_b]			+10% -10%
✖The Side C of Triangle is the length of the side C of the three sides. In other words, side C of the Triangle is the side opposite to angle C.ⓘ Side C of Triangle [S_c]			+10% -10%
✖Angle A of Triangle is the measure of the wideness of two sides that join to form the corner, opposite to the side A of the Triangle.ⓘ Angle A of Triangle [∠A]			+10% -10%

✖The Side A of Triangle is the length of the side A, of the three sides of the triangle. In other words, the side A of the Triangle is the side opposite to the angle A.ⓘ Side A of Triangle [S_a]

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Formula

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Side A of Triangle

Formula

`"S"_{"a"} = sqrt("S"_{"b"}^2+"S"_{"c"}^2-2*"S"_{"b"}*"S"_{"c"}*cos("∠A"))`

Example

`"10.53688m"=sqrt(("14m")^2+("20m")^2-2*"14m"*"20m"*cos("30°"))`

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Side A of Triangle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Side A of Triangle = sqrt(Side B of Triangle^2+Side C of Triangle^2-2*Side B of Triangle*Side C of Triangle*cos(Angle A of Triangle))
S_a = sqrt(S_b^2+S_c^2-2*S_b*S_c*cos(∠A))
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

Side A of Triangle - (Measured in Meter) - The Side A of Triangle is the length of the side A, of the three sides of the triangle. In other words, the side A of the Triangle is the side opposite to the angle A.
Side B of Triangle - (Measured in Meter) - The Side B of Triangle is the length of the side B of the three sides. In other words, the side Bof the Triangle is the side opposite to the angle B.
Side C of Triangle - (Measured in Meter) - The Side C of Triangle is the length of the side C of the three sides. In other words, side C of the Triangle is the side opposite to angle C.
Angle A of Triangle - (Measured in Radian) - Angle A of Triangle is the measure of the wideness of two sides that join to form the corner, opposite to the side A of the Triangle.

STEP 1: Convert Input(s) to Base Unit

Side B of Triangle: 14 Meter --> 14 Meter No Conversion Required
Side C of Triangle: 20 Meter --> 20 Meter No Conversion Required
Angle A of Triangle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_a = sqrt(S_b^2+S_c^2-2*S_b*S_c*cos(∠A)) --> sqrt(14^2+20^2-2*14*20*cos(0.5235987755982))

Evaluating ... ...

S_a = 10.5368768561047

STEP 3: Convert Result to Output's Unit

10.5368768561047 Meter --> No Conversion Required

FINAL ANSWER

10.5368768561047 ≈ 10.53688 Meter <-- Side A of Triangle

(Calculation completed in 00.004 seconds)

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< 13 Side of Triangle Calculators

Side A of Triangle

Go Side A of Triangle = sqrt(Side B of Triangle^2+Side C of Triangle^2-2*Side B of Triangle*Side C of Triangle*cos(Angle A of Triangle))

Side B of Triangle

Go Side B of Triangle = sqrt(Side A of Triangle^2+Side C of Triangle^2-2*Side A of Triangle*Side C of Triangle*cos(Angle B of Triangle))

Side C of Triangle

Go Side C of Triangle = sqrt(Side B of Triangle^2+Side A of Triangle^2-2*Side A of Triangle*Side B of Triangle*cos(Angle C of Triangle))

Side A of Triangle given Two Angles and Side B

Go Side A of Triangle = Side B of Triangle*sin(Angle A of Triangle)/sin(Angle B of Triangle)

Side B of Triangle given Two Angles and Side A

Go Side B of Triangle = Side A of Triangle*sin(Angle B of Triangle)/sin(Angle A of Triangle)

Side C of Triangle given Two Angles and Side B

Go Side C of Triangle = Side B of Triangle*sin(Angle C of Triangle)/sin(Angle B of Triangle)

Side A of Triangle given Two Angles and Side C

Go Side A of Triangle = Side C of Triangle*sin(Angle A of Triangle)/sin(Angle C of Triangle)

Side B of Triangle given Two Angles and Side C

Go Side B of Triangle = Side C of Triangle*sin(Angle B of Triangle)/sin(Angle C of Triangle)

Side C of Triangle given Two Angles and Side A

Go Side C of Triangle = Side A of Triangle*sin(Angle C of Triangle)/sin(Angle A of Triangle)

Side A of Triangle given Side B , Sin C and Area of Triangle

Go Side A of Triangle = (2*Area of Triangle)/(Side B of Triangle*Sin C)

Side A of Triangle given Side C , Sin B and Area of Triangle

Go Side A of Triangle = (2*Area of Triangle)/(Side C of Triangle*Sin B)

Side B of Triangle given Side C , Sin A and Area of Triangle

Go Side B of Triangle = (2*Area of Triangle)/(Side C of Triangle*Sin A)

Side B of Triangle given Side A , Sin C and Area of Triangle

Go Side B of Triangle = (2*Area of Triangle)/(Side A of Triangle*Sin C)

< 4 Sides of Triangle Calculators

Side A of Triangle

Go Side A of Triangle = sqrt(Side B of Triangle^2+Side C of Triangle^2-2*Side B of Triangle*Side C of Triangle*cos(Angle A of Triangle))

Side B of Triangle

Go Side B of Triangle = sqrt(Side A of Triangle^2+Side C of Triangle^2-2*Side A of Triangle*Side C of Triangle*cos(Angle B of Triangle))

Side C of Triangle

Go Side C of Triangle = sqrt(Side B of Triangle^2+Side A of Triangle^2-2*Side A of Triangle*Side B of Triangle*cos(Angle C of Triangle))

Side A of Triangle given Two Angles and Side B

Go Side A of Triangle = Side B of Triangle*sin(Angle A of Triangle)/sin(Angle B of Triangle)

Side A of Triangle Formula

Side A of Triangle = sqrt(Side B of Triangle^2+Side C of Triangle^2-2*Side B of Triangle*Side C of Triangle*cos(Angle A of Triangle))
S_a = sqrt(S_b^2+S_c^2-2*S_b*S_c*cos(∠A))

What is a Triangle?

The Triangle is the type of polygon, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

How to Calculate Side A of Triangle?

Side A of Triangle calculator uses Side A of Triangle = sqrt(Side B of Triangle^2+Side C of Triangle^2-2*Side B of Triangle*Side C of Triangle*cos(Angle A of Triangle)) to calculate the Side A of Triangle, Side A of Triangle is one of the three sides of the Triangle, calculated using the other two sides and angle A. Side A of Triangle is denoted by S_a symbol.

How to calculate Side A of Triangle using this online calculator? To use this online calculator for Side A of Triangle, enter Side B of Triangle (S_b), Side C of Triangle (S_c) & Angle A of Triangle (∠A) and hit the calculate button. Here is how the Side A of Triangle calculation can be explained with given input values -> 10.53688 = sqrt(14^2+20^2-2*14*20*cos(0.5235987755982)).

FAQ

What is Side A of Triangle?

Side A of Triangle is one of the three sides of the Triangle, calculated using the other two sides and angle A and is represented as S_a = sqrt(S_b^2+S_c^2-2*S_b*S_c*cos(∠A)) or Side A of Triangle = sqrt(Side B of Triangle^2+Side C of Triangle^2-2*Side B of Triangle*Side C of Triangle*cos(Angle A of Triangle)). The Side B of Triangle is the length of the side B of the three sides. In other words, the side Bof the Triangle is the side opposite to the angle B, The Side C of Triangle is the length of the side C of the three sides. In other words, side C of the Triangle is the side opposite to angle C & Angle A of Triangle is the measure of the wideness of two sides that join to form the corner, opposite to the side A of the Triangle.

How to calculate Side A of Triangle?

Side A of Triangle is one of the three sides of the Triangle, calculated using the other two sides and angle A is calculated using Side A of Triangle = sqrt(Side B of Triangle^2+Side C of Triangle^2-2*Side B of Triangle*Side C of Triangle*cos(Angle A of Triangle)). To calculate Side A of Triangle, you need Side B of Triangle (S_b), Side C of Triangle (S_c) & Angle A of Triangle (∠A). With our tool, you need to enter the respective value for Side B of Triangle, Side C of Triangle & Angle A of 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 Side A of Triangle?

In this formula, Side A of Triangle uses Side B of Triangle, Side C of Triangle & Angle A of Triangle. We can use 5 other way(s) to calculate the same, which is/are as follows -

Side A of Triangle = Side B of Triangle*sin(Angle A of Triangle)/sin(Angle B of Triangle)
Side A of Triangle = Side C of Triangle*sin(Angle A of Triangle)/sin(Angle C of Triangle)
Side A of Triangle = (2*Area of Triangle)/(Side B of Triangle*Sin C)
Side A of Triangle = (2*Area of Triangle)/(Side C of Triangle*Sin B)
Side A of Triangle = Side B of Triangle*sin(Angle A of Triangle)/sin(Angle B of Triangle)

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