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Exradius Opposite to Angle A of Triangle Formula

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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. Check FAQs

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}}}

r_e(∠A) - Exradius Opposite to ∠A of Triangle?S_a - Side A of Triangle?S_b - Side B of Triangle?S_c - Side C of Triangle?

Exradius Opposite to Angle A of Triangle Example

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Here is how the Exradius Opposite to Angle A of Triangle equation looks like with Values.

Here is how the Exradius Opposite to Angle A of Triangle equation looks like with Units.

Here is how the Exradius Opposite to Angle A of Triangle equation looks like.

5.416 = \sqrt{\frac{(\frac{10 + 14 + 20}{2}) \cdot (\frac{10 - 14 + 20}{2}) \cdot (\frac{10 + 14 - 20}{2})}{\frac{14 + 20 - 10}{2}}}

5.416m = \sqrt{\frac{(\frac{10m + 14m + 20m}{2}) \cdot (\frac{10m - 14m + 20m}{2}) \cdot (\frac{10m + 14m - 20m}{2})}{\frac{14m + 20m - 10m}{2}}}

5.416 = \sqrt{\frac{(\frac{10 + 14 + 20}{2}) \cdot (\frac{10 - 14 + 20}{2}) \cdot (\frac{10 + 14 - 20}{2})}{\frac{14 + 20 - 10}{2}}}

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Exradius Opposite to Angle A of Triangle Solution

Follow our step by step solution on how to calculate Exradius Opposite to Angle A of Triangle?

FIRST Step Consider the formula

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}}}

Next Step Substitute values of Variables

∴

r e(∠A) = \sqrt{\frac{(\frac{10m + 14m + 20m}{2}) \cdot (\frac{10m - 14m + 20m}{2}) \cdot (\frac{10m + 14m - 20m}{2})}{\frac{14m + 20m - 10m}{2}}}

Next Step Prepare to Evaluate

∴

r e(∠A) = \sqrt{\frac{(\frac{10 + 14 + 20}{2}) \cdot (\frac{10 - 14 + 20}{2}) \cdot (\frac{10 + 14 - 20}{2})}{\frac{14 + 20 - 10}{2}}}

Next Step Evaluate

∴

r e(∠A) = 5.41602560309064m

LAST Step Rounding Answer

∴

r e(∠A) = 5.416m

Exradius Opposite to Angle A of Triangle Formula Elements

Variables

Functions

Exradius Opposite to ∠A of Triangle

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.

Symbol: r_e(∠A)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Exradius Opposite to ∠A 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

Side B 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.

Symbol: S_b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side B of Triangle

Side C of Triangle

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.

Symbol: S_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side C of Triangle

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.

Syntax: sqrt(Number)

Other formulas in Radius of Triangle category

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)}}

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)}

How to Evaluate Exradius Opposite to Angle A of Triangle?

Exradius Opposite to Angle A of Triangle evaluator 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 evaluate 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 evaluate Exradius Opposite to Angle A of Triangle using this online evaluator? To use this online evaluator 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.

FAQs on Exradius Opposite to Angle A of Triangle

What is the formula to find Exradius Opposite to Angle A of Triangle?

The formula of Exradius Opposite to Angle A of Triangle is expressed as 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)). Here is an example- 5.416026 = sqrt((((10+14+20)/2)*((10-14+20)/2)*((10+14-20)/2))/((14+20-10)/2)).

How to calculate Exradius Opposite to Angle A of Triangle?

With Side A of Triangle (S_a), Side B of Triangle (S_b) & Side C of Triangle (S_c) we can find Exradius Opposite to Angle A of Triangle using the formula - 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)). This formula also uses Square Root (sqrt) function(s).

Can the Exradius Opposite to Angle A of Triangle be negative?

No, the Exradius Opposite to Angle A of Triangle, measured in Length cannot be negative.

Which unit is used to measure Exradius Opposite to Angle A of Triangle?

Exradius Opposite to Angle A of Triangle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Exradius Opposite to Angle A of Triangle can be measured.

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Exradius Opposite to Angle A of Triangle Formula

Exradius Opposite to Angle A of Triangle Example

Exradius Opposite to Angle A of Triangle Solution

Exradius Opposite to Angle A of Triangle Formula Elements

Other formulas in Radius of Triangle category

How to Evaluate Exradius Opposite to Angle A of Triangle?

FAQs on Exradius Opposite to Angle A of Triangle

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