Exradius Opposite to Angle A of Triangle Calculator

✖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]			+10% -10%
✖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%

✖The Exradius Opposite to ∠A of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠A and external angle bisectors of other two angles.ⓘ Exradius Opposite to Angle A of Triangle [r_e(∠A)]

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Formula

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Exradius Opposite to Angle A of Triangle

Formula

`"r"_{"e(∠A)"} = sqrt(((("S"_{"a"}+"S"_{"b"}+"S"_{"c"})/2)*(("S"_{"a"}-"S"_{"b"}+"S"_{"c"})/2)*(("S"_{"a"}+"S"_{"b"}-"S"_{"c"})/2))/(("S"_{"b"}+"S"_{"c"}-"S"_{"a"})/2))`

Example

`"5.416026m"=sqrt(((("10m"+"14m"+"20m")/2)*(("10m"-"14m"+"20m")/2)*(("10m"+"14m"-"20m")/2))/(("14m"+"20m"-"10m")/2))`

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Exradius Opposite to Angle A of Triangle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Exradius Opposite to ∠A of Triangle = sqrt((((Side A of Triangle+Side B of Triangle+Side C of Triangle)/2)*((Side A of Triangle-Side B of Triangle+Side C of Triangle)/2)*((Side A of Triangle+Side B of Triangle-Side C of Triangle)/2))/((Side B of Triangle+Side C of Triangle-Side A of Triangle)/2))
r_e(∠A) = sqrt((((S_a+S_b+S_c)/2)*((S_a-S_b+S_c)/2)*((S_a+S_b-S_c)/2))/((S_b+S_c-S_a)/2))
This formula uses 1 Functions, 4 Variables

Functions Used

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

Exradius Opposite to ∠A of Triangle - (Measured in Meter) - The Exradius Opposite to ∠A of triangle is the radius of circle formed with center as point of intersection of internal angle bisector of ∠A and external angle bisectors of other two angles.
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.

STEP 1: Convert Input(s) to Base Unit

Side A of Triangle: 10 Meter --> 10 Meter No Conversion Required
Side B of Triangle: 14 Meter --> 14 Meter No Conversion Required
Side C of Triangle: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_e(∠A) = sqrt((((S_a+S_b+S_c)/2)*((S_a-S_b+S_c)/2)*((S_a+S_b-S_c)/2))/((S_b+S_c-S_a)/2)) --> sqrt((((10+14+20)/2)*((10-14+20)/2)*((10+14-20)/2))/((14+20-10)/2))

Evaluating ... ...

r_e(∠A) = 5.41602560309064

STEP 3: Convert Result to Output's Unit

5.41602560309064 Meter --> No Conversion Required

FINAL ANSWER

5.41602560309064 ≈ 5.416026 Meter <-- Exradius Opposite to ∠A of Triangle

(Calculation completed in 00.004 seconds)

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Credits

Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

Dhruv Walia has created this Calculator and 1100+ more calculators!

Verified by Nikhil

Mumbai University (DJSCE), Mumbai

Nikhil has verified this Calculator and 300+ more calculators!

< 7 Radius of Triangle Calculators

Circumradius of Triangle

Go Circumradius of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle-Side A of Triangle+Side C of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle))

Inradius of Triangle

Go Inradius of Triangle = sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle+Side C of Triangle-Side A of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle))/(2*(Side A of Triangle+Side B of Triangle+Side C of Triangle))

Exradius Opposite to Angle A of Triangle

Go Exradius Opposite to ∠A of Triangle = sqrt((((Side A of Triangle+Side B of Triangle+Side C of Triangle)/2)*((Side A of Triangle-Side B of Triangle+Side C of Triangle)/2)*((Side A of Triangle+Side B of Triangle-Side C of Triangle)/2))/((Side B of Triangle+Side C of Triangle-Side A of Triangle)/2))

Inradius of Triangle by Heron's Formula

Go Inradius of Triangle = sqrt(((Semiperimeter of Triangle-Side C of Triangle)*(Semiperimeter of Triangle-Side B of Triangle)*(Semiperimeter of Triangle-Side A of Triangle))/Semiperimeter of Triangle)

Circumradius of Triangle given Three Exradii and Inradius

Go Circumradius of Triangle = (Exradius Opposite to ∠A of Triangle+Exradius Opposite to ∠B of Triangle+Exradius Opposite to ∠C of Triangle-Inradius of Triangle)/4

Inradius of Triangle given Three Exradii

Go Inradius of Triangle = 1/(1/Exradius Opposite to ∠A of Triangle+1/Exradius Opposite to ∠B of Triangle+1/Exradius Opposite to ∠C of Triangle)

Circumradius of Triangle given One Side and its Opposite Angle

Go Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle))

< 3 Radius of Triangle Calculators

Circumradius of Triangle

Inradius of Triangle

Exradius Opposite to Angle A of Triangle

Exradius Opposite to Angle A of Triangle Formula

What is a Triangle?

A Triangle is a 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.

What is Excircle of Triangle?

An excircle of a triangle is a circle that lies outside the triangle and is tangent to one of its sides, and the extensions of the other two sides. Each triangle has three excircles, one for each of its sides. The center of an excircle is called an excenter.

How to Calculate Exradius Opposite to Angle A of Triangle?

Exradius Opposite to Angle A of Triangle calculator uses Exradius Opposite to ∠A of Triangle = sqrt((((Side A of Triangle+Side B of Triangle+Side C of Triangle)/2)*((Side A of Triangle-Side B of Triangle+Side C of Triangle)/2)*((Side A of Triangle+Side B of Triangle-Side C of Triangle)/2))/((Side B of Triangle+Side C of Triangle-Side A of Triangle)/2)) to calculate the Exradius Opposite to ∠A of Triangle, The Exradius Opposite to Angle A of Triangle formula is defined as the radius of circle formed with center as point of intersection of internal angle bisector of ∠A and external angle bisectors of other two angles. Exradius Opposite to ∠A of Triangle is denoted by r_e(∠A) symbol.

How to calculate Exradius Opposite to Angle A of Triangle using this online calculator? To use this online calculator for Exradius Opposite to Angle A of Triangle, enter Side A of Triangle (S_a), Side B of Triangle (S_b) & Side C of Triangle (S_c) and hit the calculate button. Here is how the Exradius Opposite to Angle A of Triangle calculation can be explained with given input values -> 5.416026 = sqrt((((10+14+20)/2)*((10-14+20)/2)*((10+14-20)/2))/((14+20-10)/2)).

FAQ

What is Exradius Opposite to Angle A of Triangle?

The Exradius Opposite to Angle A of Triangle formula is defined as the radius of circle formed with center as point of intersection of internal angle bisector of ∠A and external angle bisectors of other two angles and is represented as r_e(∠A) = sqrt((((S_a+S_b+S_c)/2)*((S_a-S_b+S_c)/2)*((S_a+S_b-S_c)/2))/((S_b+S_c-S_a)/2)) or Exradius Opposite to ∠A of Triangle = sqrt((((Side A of Triangle+Side B of Triangle+Side C of Triangle)/2)*((Side A of Triangle-Side B of Triangle+Side C of Triangle)/2)*((Side A of Triangle+Side B of Triangle-Side C of Triangle)/2))/((Side B of Triangle+Side C of Triangle-Side A of Triangle)/2)). 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, 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.

How to calculate Exradius Opposite to Angle A of Triangle?

The Exradius Opposite to Angle A of Triangle formula is defined as the radius of circle formed with center as point of intersection of internal angle bisector of ∠A and external angle bisectors of other two angles is calculated using Exradius Opposite to ∠A of Triangle = sqrt((((Side A of Triangle+Side B of Triangle+Side C of Triangle)/2)*((Side A of Triangle-Side B of Triangle+Side C of Triangle)/2)*((Side A of Triangle+Side B of Triangle-Side C of Triangle)/2))/((Side B of Triangle+Side C of Triangle-Side A of Triangle)/2)). To calculate Exradius Opposite to Angle A of Triangle, you need Side A of Triangle (S_a), Side B of Triangle (S_b) & Side C of Triangle (S_c). With our tool, you need to enter the respective value for Side A of Triangle, Side B of Triangle & Side C of Triangle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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