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Circumradius of Triangle given One Side and its Opposite Angle Formula

GoCircumradius of Triangle given Three Exradii and Inradius Formula

GoCircumradius of Triangle Formula

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Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle. Check FAQs

r c = \frac{S a}{2 \cdot \sin (∠A)}

r_c - Circumradius of Triangle?S_a - Side A of Triangle?∠A - Angle A of Triangle?

Circumradius of Triangle given One Side and its Opposite Angle Example

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Here is how the Circumradius of Triangle given One Side and its Opposite Angle equation looks like with Values.

Here is how the Circumradius of Triangle given One Side and its Opposite Angle equation looks like with Units.

Here is how the Circumradius of Triangle given One Side and its Opposite Angle equation looks like.

10 = \frac{10}{2 \cdot \sin (30)}

10m = \frac{10m}{2 \cdot \sin (30°)}

10 = \frac{10}{2 \cdot \sin (30)}

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Circumradius of Triangle given One Side and its Opposite Angle Solution

Follow our step by step solution on how to calculate Circumradius of Triangle given One Side and its Opposite Angle?

FIRST Step Consider the formula

r c = \frac{S a}{2 \cdot \sin (∠A)}

Next Step Substitute values of Variables

∴

r c = \frac{10m}{2 \cdot \sin (30°)}

Next Step Convert Units

∴

r c = \frac{10m}{2 \cdot \sin (0.5236rad)}

Next Step Prepare to Evaluate

∴

r c = \frac{10}{2 \cdot \sin (0.5236)}

LAST Step Evaluate

∴

r c = 10m

Circumradius of Triangle given One Side and its Opposite Angle Formula Elements

Variables

Functions

Circumradius of Triangle

Circumradius of Triangle is the radius of a circumcircle touching each of the vertices of the Triangle.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Triangle

Side 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.

Symbol: S_a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side A of Triangle

Angle A of Triangle

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.

Symbol: ∠A

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle A of Triangle

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.

Syntax: sin(Angle)

Other Formulas to find Circumradius of Triangle

Go Circumradius of Triangle given Three Exradii and Inradius

r c = \frac{r e(∠A) + r e(∠B) + r e(∠C) - r i}{4}

Go Circumradius of Triangle

r c = \frac{S a \cdot S b \cdot S c}{\sqrt{(S a + S b + S c) \cdot (S b - S a + S c) \cdot (S a - S b + S c) \cdot (S a + S b - S c)}}

Other formulas in Radius of Triangle category

Go Inradius of Triangle given Three Exradii

r i = \frac{1}{\frac{1}{r e(∠A)} + \frac{1}{r e(∠B)} + \frac{1}{r e(∠C)}}

Go Inradius of Triangle

r i = \frac{\sqrt{(S a + S b + S c) \cdot (S b + S c - S a) \cdot (S a - S b + S c) \cdot (S a + S b - S c)}}{2 \cdot (S a + S b + S c)}

Go Exradius Opposite to Angle A of Triangle

r e(∠A) = \sqrt{\frac{(\frac{S a + S b + S c}{2}) \cdot (\frac{S a - S b + S c}{2}) \cdot (\frac{S a + S b - S c}{2})}{\frac{S b + S c - S a}{2}}}

Go Inradius of Triangle by Heron's Formula

r i = \sqrt{\frac{(s - S c) \cdot (s - S b) \cdot (s - S a)}{s}}

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

Circumradius of Triangle given One Side and its Opposite Angle evaluator uses Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle)) to evaluate 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 evaluate Circumradius of Triangle given One Side and its Opposite Angle using this online evaluator? To use this online evaluator 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.

FAQs on Circumradius of Triangle given One Side and its Opposite Angle

What is the formula to find Circumradius of Triangle given One Side and its Opposite Angle?

The formula of Circumradius of Triangle given One Side and its Opposite Angle is expressed as Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle)). Here is an example- 10 = 10/(2*sin(0.5235987755982)).

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

With Side A of Triangle (S_a) & Angle A of Triangle (∠A) we can find Circumradius of Triangle given One Side and its Opposite Angle using the formula - Circumradius of Triangle = Side A of Triangle/(2*sin(Angle A of Triangle)). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Circumradius of Triangle?

Here are the different ways to Calculate Circumradius of Triangle-

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))

Can the Circumradius of Triangle given One Side and its Opposite Angle be negative?

No, the Circumradius of Triangle given One Side and its Opposite Angle, measured in Length cannot be negative.

Which unit is used to measure Circumradius of Triangle given One Side and its Opposite Angle?

Circumradius of Triangle given One Side and its Opposite Angle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Circumradius of Triangle given One Side and its Opposite Angle can be measured.

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Circumradius of Triangle given One Side and its Opposite Angle Formula

​GoCircumradius of Triangle given Three Exradii and Inradius Formula

​GoCircumradius of Triangle Formula

Circumradius of Triangle given One Side and its Opposite Angle Example

Circumradius of Triangle given One Side and its Opposite Angle Solution

Circumradius of Triangle given One Side and its Opposite Angle Formula Elements

Other Formulas to find Circumradius of Triangle

Other formulas in Radius of Triangle category

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

FAQs on Circumradius of Triangle given One Side and its Opposite Angle

Variable Name

GoCircumradius of Triangle given Three Exradii and Inradius Formula

GoCircumradius of Triangle Formula