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Inradius of Isosceles Triangle given Legs and Height Formula

GoInradius of Isosceles Triangle Formula

GoCircumradius of Isosceles Triangle Formula

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The Inradius of Isosceles Triangle is defined as the radius of the circle inscribed inside the Isosceles Triangle. Check FAQs

r i = \frac{h \cdot \sqrt{{S Legs}^{2} - h^{2}}}{S Legs + \sqrt{{S Legs}^{2} - h^{2}}}

r_i - Inradius of Isosceles Triangle?h - Height of Isosceles Triangle?S_Legs - Legs of Isosceles Triangle?

Inradius of Isosceles Triangle given Legs and Height Example

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Here is how the Inradius of Isosceles Triangle given Legs and Height equation looks like with Values.

Here is how the Inradius of Isosceles Triangle given Legs and Height equation looks like with Units.

Here is how the Inradius of Isosceles Triangle given Legs and Height equation looks like.

2.5135 = \frac{8 \cdot \sqrt{9^{2} - 8^{2}}}{9 + \sqrt{9^{2} - 8^{2}}}

2.5135m = \frac{8m \cdot \sqrt{{9m}^{2} - {8m}^{2}}}{9m + \sqrt{{9m}^{2} - {8m}^{2}}}

2.5135 = \frac{8 \cdot \sqrt{9^{2} - 8^{2}}}{9 + \sqrt{9^{2} - 8^{2}}}

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Inradius of Isosceles Triangle given Legs and Height Solution

Follow our step by step solution on how to calculate Inradius of Isosceles Triangle given Legs and Height?

FIRST Step Consider the formula

r i = \frac{h \cdot \sqrt{{S Legs}^{2} - h^{2}}}{S Legs + \sqrt{{S Legs}^{2} - h^{2}}}

Next Step Substitute values of Variables

∴

r i = \frac{8m \cdot \sqrt{{9m}^{2} - {8m}^{2}}}{9m + \sqrt{{9m}^{2} - {8m}^{2}}}

Next Step Prepare to Evaluate

∴

r i = \frac{8 \cdot \sqrt{9^{2} - 8^{2}}}{9 + \sqrt{9^{2} - 8^{2}}}

Next Step Evaluate

∴

r i = 2.51349382881987m

LAST Step Rounding Answer

∴

r i = 2.5135m

Inradius of Isosceles Triangle given Legs and Height Formula Elements

Variables

Functions

Inradius of Isosceles Triangle

The Inradius of Isosceles Triangle is defined as the radius of the circle inscribed inside the Isosceles Triangle.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Isosceles Triangle

Height of Isosceles Triangle

The Height of Isosceles Triangle is the perpendicular distance from the base of the triangle to the opposite vertex.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Isosceles Triangle

Legs of Isosceles Triangle

The Legs of Isosceles Triangle are the two equal sides of the Isosceles Triangle.

Symbol: S_Legs

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Legs of Isosceles 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 to find Inradius of Isosceles Triangle

Go Inradius of Isosceles Triangle

r i = \frac{S Base}{2} \cdot \sqrt{\frac{2 \cdot S Legs - S Base}{2 \cdot S Legs + S Base}}

Go Circumradius of Isosceles Triangle

r i = \frac{{S Legs}^{2}}{\sqrt{4 \cdot {S Legs}^{2} - {S Base}^{2}}}

Go Inradius of Isosceles Triangle given Legs and Base Angle

r i = S Legs \cdot \cos (∠ Base) \cdot \tan (\frac{∠ Base}{2})

Go Inradius of Isosceles Triangle given Base and Base Angle

r i = \frac{S Base}{2} \cdot \tan (\frac{∠ Base}{2})

Other formulas in Radius of Isosceles Triangle category

Go Circumradius of Isosceles Triangle given Legs and Height

r c = \frac{{S Legs}^{2}}{2 \cdot h}

How to Evaluate Inradius of Isosceles Triangle given Legs and Height?

Inradius of Isosceles Triangle given Legs and Height evaluator uses Inradius of Isosceles Triangle = (Height of Isosceles Triangle*sqrt(Legs of Isosceles Triangle^2-Height of Isosceles Triangle^2))/(Legs of Isosceles Triangle+sqrt(Legs of Isosceles Triangle^2-Height of Isosceles Triangle^2)) to evaluate the Inradius of Isosceles Triangle, The Inradius of Isosceles Triangle given Legs and Height formula is defined as the length of the radius of the incircle of the Isosceles Triangle, calculated using its legs and height. Inradius of Isosceles Triangle is denoted by r_i symbol.

How to evaluate Inradius of Isosceles Triangle given Legs and Height using this online evaluator? To use this online evaluator for Inradius of Isosceles Triangle given Legs and Height, enter Height of Isosceles Triangle (h) & Legs of Isosceles Triangle (S_Legs) and hit the calculate button.

FAQs on Inradius of Isosceles Triangle given Legs and Height

What is the formula to find Inradius of Isosceles Triangle given Legs and Height?

The formula of Inradius of Isosceles Triangle given Legs and Height is expressed as Inradius of Isosceles Triangle = (Height of Isosceles Triangle*sqrt(Legs of Isosceles Triangle^2-Height of Isosceles Triangle^2))/(Legs of Isosceles Triangle+sqrt(Legs of Isosceles Triangle^2-Height of Isosceles Triangle^2)). Here is an example- 2.513494 = (8*sqrt(9^2-8^2))/(9+sqrt(9^2-8^2)).

How to calculate Inradius of Isosceles Triangle given Legs and Height?

With Height of Isosceles Triangle (h) & Legs of Isosceles Triangle (S_Legs) we can find Inradius of Isosceles Triangle given Legs and Height using the formula - Inradius of Isosceles Triangle = (Height of Isosceles Triangle*sqrt(Legs of Isosceles Triangle^2-Height of Isosceles Triangle^2))/(Legs of Isosceles Triangle+sqrt(Legs of Isosceles Triangle^2-Height of Isosceles Triangle^2)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Inradius of Isosceles Triangle?

Here are the different ways to Calculate Inradius of Isosceles Triangle-

Inradius of Isosceles Triangle=Base of Isosceles Triangle/2*sqrt((2*Legs of Isosceles Triangle-Base of Isosceles Triangle)/(2*Legs of Isosceles Triangle+Base of Isosceles Triangle))
Inradius of Isosceles Triangle=Legs of Isosceles Triangle^2/sqrt(4*Legs of Isosceles Triangle^2-Base of Isosceles Triangle^2)
Inradius of Isosceles Triangle=Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2)

Can the Inradius of Isosceles Triangle given Legs and Height be negative?

No, the Inradius of Isosceles Triangle given Legs and Height, measured in Length cannot be negative.

Which unit is used to measure Inradius of Isosceles Triangle given Legs and Height?

Inradius of Isosceles Triangle given Legs and Height is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Inradius of Isosceles Triangle given Legs and Height can be measured.

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Inradius of Isosceles Triangle given Legs and Height Formula

​GoInradius of Isosceles Triangle Formula

​GoCircumradius of Isosceles Triangle Formula

Inradius of Isosceles Triangle given Legs and Height Example

Inradius of Isosceles Triangle given Legs and Height Solution

Inradius of Isosceles Triangle given Legs and Height Formula Elements

Other Formulas to find Inradius of Isosceles Triangle

Other formulas in Radius of Isosceles Triangle category

How to Evaluate Inradius of Isosceles Triangle given Legs and Height?

FAQs on Inradius of Isosceles Triangle given Legs and Height

Variable Name

GoInradius of Isosceles Triangle Formula

GoCircumradius of Isosceles Triangle Formula