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))
rc = Sa/(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
rc = Sa/(2*sin(∠A)) --> 10/(2*sin(0.5235987755982))
Evaluating ... ...
rc = 10
STEP 3: Convert Result to Output's Unit
10 Meter --> No Conversion Required
FINAL ANSWER
10 Meter <-- Circumradius of Triangle
(Calculation completed in 00.006 seconds)

Credits

Creator Image
Created by Mona Gladys
St Joseph's College (SJC), Bengaluru
Mona Gladys has created this Calculator and 2000+ more calculators!
Verifier Image
Verified by Shweta Patil
Walchand College of Engineering (WCE), Sangli
Shweta Patil has verified this Calculator and 1100+ more calculators!

Radius of Triangle Calculators

Circumradius of Triangle
​ LaTeX ​ 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))
Circumradius of Triangle given Three Exradii and Inradius
​ LaTeX ​ 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
​ LaTeX ​ 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
​ LaTeX ​ 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

​LaTeX ​Go
Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle))
rc = Sa/(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 rc 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 (Sa) & 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 rc = Sa/(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 (Sa) & 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))
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!