Inradius of Isosceles Triangle given Legs and Base Angle Calculator

✖The Legs of Isosceles Triangle are the two equal sides of the Isosceles Triangle.ⓘ Legs of Isosceles Triangle [S_Legs]			+10% -10%
✖Base Angles of Isosceles Triangle are the equal angles between the base and the legs of the Isosceles Triangle.ⓘ Base Angles of Isosceles Triangle [∠_Base]			+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 Base Angle [r_i]

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Inradius of Isosceles Triangle given Legs and Base Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Isosceles Triangle = Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2)
r_i = S_Legs*cos(∠_Base)*tan(∠_Base/2)
This formula uses 2 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)

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.
Legs of Isosceles Triangle - (Measured in Meter) - The Legs of Isosceles Triangle are the two equal sides of the Isosceles Triangle.
Base Angles of Isosceles Triangle - (Measured in Radian) - Base Angles of Isosceles Triangle are the equal angles between the base and the legs of the Isosceles Triangle.

STEP 1: Convert Input(s) to Base Unit

Legs of Isosceles Triangle: 9 Meter --> 9 Meter No Conversion Required
Base Angles of Isosceles Triangle: 70 Degree --> 1.2217304763958 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = S_Legs*cos(∠_Base)*tan(∠_Base/2) --> 9*cos(1.2217304763958)*tan(1.2217304763958/2)

Evaluating ... ...

r_i = 2.15536574318662

STEP 3: Convert Result to Output's Unit

2.15536574318662 Meter --> No Conversion Required

FINAL ANSWER

2.15536574318662 ≈ 2.155366 Meter <-- Inradius of Isosceles Triangle

(Calculation completed in 00.019 seconds)

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< Radius of Isosceles Triangle Calculators

Inradius of Isosceles Triangle

LaTeX 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

LaTeX 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

LaTeX Go Inradius of Isosceles Triangle = Legs of Isosceles Triangle^2/sqrt(4*Legs of Isosceles Triangle^2-Base of Isosceles Triangle^2)

Circumradius of Isosceles Triangle given Legs and Height

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

< Radius of Isosceles Triangle Calculators

Inradius of Isosceles Triangle given Base and Height

LaTeX Go Inradius of Isosceles Triangle = (Base of Isosceles Triangle*Height of Isosceles Triangle)/(Base of Isosceles Triangle+sqrt(4*Height of Isosceles Triangle^2+Base of Isosceles Triangle^2))

Inradius of Isosceles Triangle

LaTeX 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

LaTeX 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

LaTeX 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 Legs and Base Angle Formula

LaTeX Go

Inradius of Isosceles Triangle = Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2)
r_i = S_Legs*cos(∠_Base)*tan(∠_Base/2)

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 Base Angle?

Inradius of Isosceles Triangle given Legs and Base Angle calculator uses Inradius of Isosceles Triangle = Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2) to calculate the Inradius of Isosceles Triangle, The Inradius of Isosceles Triangle given Legs and Base Angle formula is defined as the length of the radius of the incircle of Isosceles Triangle, calculated using its legs and base angle. Inradius of Isosceles Triangle is denoted by r_i symbol.

How to calculate Inradius of Isosceles Triangle given Legs and Base Angle using this online calculator? To use this online calculator for Inradius of Isosceles Triangle given Legs and Base Angle, enter Legs of Isosceles Triangle (S_Legs) & Base Angles of Isosceles Triangle (∠_Base) and hit the calculate button. Here is how the Inradius of Isosceles Triangle given Legs and Base Angle calculation can be explained with given input values -> 2.155366 = 9*cos(1.2217304763958)*tan(1.2217304763958/2).

FAQ

What is Inradius of Isosceles Triangle given Legs and Base Angle?

The Inradius of Isosceles Triangle given Legs and Base Angle formula is defined as the length of the radius of the incircle of Isosceles Triangle, calculated using its legs and base angle and is represented as r_i = S_Legs*cos(∠_Base)*tan(∠_Base/2) or Inradius of Isosceles Triangle = Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2). The Legs of Isosceles Triangle are the two equal sides of the Isosceles Triangle & Base Angles of Isosceles Triangle are the equal angles between the base and the legs of the Isosceles Triangle.

How to calculate Inradius of Isosceles Triangle given Legs and Base Angle?

The Inradius of Isosceles Triangle given Legs and Base Angle formula is defined as the length of the radius of the incircle of Isosceles Triangle, calculated using its legs and base angle is calculated using Inradius of Isosceles Triangle = Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2). To calculate Inradius of Isosceles Triangle given Legs and Base Angle, you need Legs of Isosceles Triangle (S_Legs) & Base Angles of Isosceles Triangle (∠_Base). With our tool, you need to enter the respective value for Legs of Isosceles Triangle & Base Angles 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 Legs of Isosceles Triangle & Base Angles of Isosceles Triangle. We can use 3 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 = (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))

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