Inradius of Isosceles Triangle given Legs and Height Calculator

✖The Height of Isosceles Triangle is the perpendicular distance from the base of the triangle to the opposite vertex.ⓘ Height of Isosceles Triangle [h]			+10% -10%
✖The Legs of Isosceles Triangle are the two equal sides of the Isosceles Triangle.ⓘ Legs of Isosceles Triangle [S_Legs]			+10% -10%

✖The Inradius of Isosceles Triangle is defined as the radius of the circle inscribed inside the Isosceles Triangle.ⓘ Inradius of Isosceles Triangle given Legs and Height [r_i]

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Inradius of Isosceles Triangle given Legs and Height

Formula

`"r"_{"i"} = ("h"*sqrt("S"_{"Legs"}^2-"h"^2))/("S"_{"Legs"}+sqrt("S"_{"Legs"}^2-"h"^2))`

Example

`"2.513494m"=("8m"*sqrt(("9m")^2-("8m")^2))/("9m"+sqrt(("9m")^2-("8m")^2))`

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Inradius of Isosceles Triangle given Legs and Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
r_i = (h*sqrt(S_Legs^2-h^2))/(S_Legs+sqrt(S_Legs^2-h^2))
This formula uses 1 Functions, 3 Variables

Functions Used

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., sqrt(Number)

Variables Used

Inradius of Isosceles Triangle - (Measured in Meter) - The Inradius of Isosceles Triangle is defined as the radius of the circle inscribed inside the Isosceles Triangle.
Height of Isosceles Triangle - (Measured in Meter) - The Height of Isosceles Triangle is the perpendicular distance from the base of the triangle to the opposite vertex.
Legs of Isosceles Triangle - (Measured in Meter) - The Legs of Isosceles Triangle are the two equal sides of the Isosceles Triangle.

STEP 1: Convert Input(s) to Base Unit

Height of Isosceles Triangle: 8 Meter --> 8 Meter No Conversion Required
Legs of Isosceles Triangle: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = (h*sqrt(S_Legs^2-h^2))/(S_Legs+sqrt(S_Legs^2-h^2)) --> (8*sqrt(9^2-8^2))/(9+sqrt(9^2-8^2))

Evaluating ... ...

r_i = 2.51349382881987

STEP 3: Convert Result to Output's Unit

2.51349382881987 Meter --> No Conversion Required

FINAL ANSWER

2.51349382881987 ≈ 2.513494 Meter <-- Inradius of Isosceles Triangle

(Calculation completed in 00.004 seconds)

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< 6 Radius of Isosceles Triangle Calculators

Inradius of Isosceles Triangle given Legs and Height

Go 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))

Inradius of Isosceles Triangle

Go 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 given Legs and Base Angle

Go Inradius of Isosceles Triangle = Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2)

Circumradius of Isosceles Triangle

Go 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 given Base and Base Angle

Go Inradius of Isosceles Triangle = Base of Isosceles Triangle/2*tan(Base Angles of Isosceles Triangle/2)

Circumradius of Isosceles Triangle given Legs and Height

Go Circumradius of Isosceles Triangle = Legs of Isosceles Triangle^2/(2*Height of Isosceles Triangle)

Inradius of Isosceles Triangle given Legs and Height Formula

What is an Isosceles Triangle?

An Isosceles Triangle is a triangle with two sides of equal length, which are called legs. The third side of the triangle is called the base. Vertex angle is the angle between the legs and the angles with the base as one of their sides are called the base angles.

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

Inradius of Isosceles Triangle given Legs and Height calculator 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 calculate 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 calculate Inradius of Isosceles Triangle given Legs and Height using this online calculator? To use this online calculator 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. Here is how the Inradius of Isosceles Triangle given Legs and Height calculation can be explained with given input values -> 2.513494 = (8*sqrt(9^2-8^2))/(9+sqrt(9^2-8^2)).

FAQ

What is Inradius of Isosceles Triangle given Legs and Height?

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 and is represented as r_i = (h*sqrt(S_Legs^2-h^2))/(S_Legs+sqrt(S_Legs^2-h^2)) or 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)). The Height of Isosceles Triangle is the perpendicular distance from the base of the triangle to the opposite vertex & The Legs of Isosceles Triangle are the two equal sides of the Isosceles Triangle.

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

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 is calculated using 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 calculate Inradius of Isosceles Triangle given Legs and Height, you need Height of Isosceles Triangle (h) & Legs of Isosceles Triangle (S_Legs). With our tool, you need to enter the respective value for Height of Isosceles Triangle & Legs of Isosceles 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 Inradius of Isosceles Triangle?

In this formula, Inradius of Isosceles Triangle uses Height of Isosceles Triangle & Legs of Isosceles Triangle. We can use 4 other way(s) to calculate the same, which is/are as follows -

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)
Inradius of Isosceles Triangle = Base of Isosceles Triangle/2*tan(Base Angles of Isosceles Triangle/2)

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