Circumradius of Triangle given One Side and its Opposite Angle 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%
✖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%

✖Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle.ⓘ Circumradius of Triangle given One Side and its Opposite Angle [r_c]

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Formula

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Circumradius of Triangle given One Side and its Opposite Angle

Formula

`"r"_{"c"} = "S"_{"a"}/(2*sin("∠A"))`

Example

`"10m"="10m"/(2*sin("30°"))`

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Circumradius of Triangle given One Side and its Opposite Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle))
r_c = S_a/(2*sin(∠A))
This formula uses 1 Functions, 3 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Circumradius of Triangle - (Measured in Meter) - Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle.
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.
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 A of Triangle: 10 Meter --> 10 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

r_c = S_a/(2*sin(∠A)) --> 10/(2*sin(0.5235987755982))

Evaluating ... ...

r_c = 10

STEP 3: Convert Result to Output's Unit

10 Meter --> No Conversion Required

FINAL ANSWER

10 Meter <-- Circumradius of Triangle

(Calculation completed in 00.004 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Walchand College of Engineering (WCE), Sangli

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< 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))

Circumradius of Triangle given One Side and its Opposite Angle Formula

Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle))
r_c = S_a/(2*sin(∠A))

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 a sine law of Triangle ?

In Triangle △ ABC, where a is the side opposite to ∠A, b opposite to ∠B, c opposite to ∠C, and where R is the circumradius, sine law states that a/sinA = b/sinB = c/sinC = 2R

How to Calculate Circumradius of Triangle given One Side and its Opposite Angle?

Circumradius of Triangle given One Side and its Opposite Angle calculator uses Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle)) to calculate the Circumradius of Triangle, Circumradius of Triangle given One Side and its Opposite Angle formula is defined as the length of the radius of the circumcircle of the triangle, calculated using one side and its opposite angle. Circumradius of Triangle is denoted by r_c symbol.

How to calculate Circumradius of Triangle given One Side and its Opposite Angle using this online calculator? To use this online calculator for Circumradius of Triangle given One Side and its Opposite Angle, enter Side A of Triangle (S_a) & Angle A of Triangle (∠A) and hit the calculate button. Here is how the Circumradius of Triangle given One Side and its Opposite Angle calculation can be explained with given input values -> 10 = 10/(2*sin(0.5235987755982)).

FAQ

What is Circumradius of Triangle given One Side and its Opposite Angle?

Circumradius of Triangle given One Side and its Opposite Angle formula is defined as the length of the radius of the circumcircle of the triangle, calculated using one side and its opposite angle and is represented as r_c = S_a/(2*sin(∠A)) or Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle)). 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 & 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 Circumradius of Triangle given One Side and its Opposite Angle?

Circumradius of Triangle given One Side and its Opposite Angle formula is defined as the length of the radius of the circumcircle of the triangle, calculated using one side and its opposite angle is calculated using Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle)). To calculate Circumradius of Triangle given One Side and its Opposite Angle, you need Side A of Triangle (S_a) & Angle A of Triangle (∠A). With our tool, you need to enter the respective value for Side A 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 Circumradius of Triangle?

In this formula, Circumradius of Triangle uses Side A of Triangle & Angle A of Triangle. We can use 2 other way(s) to calculate the same, which is/are as follows -

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
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))

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