Isosceles Triangle Solver

From the equal leg and either the base or the apex angle, find the area, perimeter, height, base and apex angles, and the inradius and circumradius.

Input

Enter the equal leg length and either the base or the apex angle to find the area, perimeter, height, angles, and inradius and circumradius of an isosceles triangle.

Equal leg length a

Second known value

Base b

Result

Area

Perimeter

Height

Leg a

Base b

Apex angle

73.739795 deg

Base angle

53.130102 deg

Inradius

Circumradius

6.25

Lengths use the same unit as the input, and the area uses that unit squared.

How it works

The triangle has two equal legs of length a and one base of length b.
When you specify the base, it must be shorter than twice the leg for the triangle to exist.
When you specify the apex angle, use a value above 0 and below 180 in degrees, or above 0 and below pi in radians.
The height is the perpendicular from the apex to the base, found from the right triangle formed by half the base and a leg.
The area equals base times height divided by 2, and the perimeter equals 2a plus b.
The apex angle comes from the law of cosines, and each base angle equals 180 degrees minus the apex angle, divided by 2.
The inradius equals the area divided by the semiperimeter, and the circumradius equals the product of the three sides divided by four times the area.
Lengths use the same unit as the input, and the area uses that unit squared.

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