Notes
Related Calculations:
[Circle Sector Calculator]
[Circle Unit Conversion]
[Angle Unit Conversion]
[Medians and Altitudes]
[Incircles and Circumcircles]

Triangle Solvers
Known:
[Three Sides]
[Right Triangle, Two Sides]
[Two Sides, Included Angle]
[Two Sides, an Opposite Angle]
[Two Angles, an Opposite Side]
[Two Angles, Included Side]

Set decimal places for all calculators.
Default = 6 decimal places
Trailing zeros are not displayed.


Entries:
Sides only required.
This calculator is included for convenience, since the right triangle is the basic element of trigomometry.
Circles are closely associated with triangles and angles,
hence a few related geometric theorems useful for layout work are noted.
Geometry:
An angle inscribed in a semicircle is a right angle.


Entries:
Enter the triangle sides, or copy and paste the side values from the other calculators,
for more detailed information about a triangle.
Interpreting returned values:
Angles:
The largest side is opposite the largest angle, the smallest side is opposite the smallest angle.
Altitudes:
The least altitude is perpendicular to the largest side, the greatest altitude is perpendicular to the shortest side.
Medians:
At their respective points of intercept, the least median is bisects the largest side, the greatest median bisects the shortest side.
Related circles:
Incircle:
The incenter is the intercept of the angle bisectors.
The incircle is tangent to the sides of the triangle.
Circumcircle:
The circumcenter is the intercept of the perpendicular bisectors of the triangle sides.
The circumcircle passes through the vertices of the triangle.


Entries:
Set the included angle at 90 degrees to return right triangle data.
Geometry:
The medians of a triangle intercept each other in a ratio of 2:1 (vertex : midpoint of opposite side)
at the centroid, the center of gravity of the triangle.

Known: Two Sides,
Included Angle

[Index]


Entries:
When using this calculator, it must be known if the triangle has an obtuse angle, and if so, this angle must be entered.
The highlighted side and angle must be opposite one another.
Entering the other known sides and an acute angle, even though their values are correct, returns inappropriate results.
Geometry:
An angle inscribed in a circle is half the value of the central angle subtended by the same arc.
Angles inscribed in a circle and subtended by the same arc are equal.

Known: Two Sides,
Angle Opposite Side

[Index]


Entries:
The highlighted side and angle must be opposite one another.
Use this calculator if Two Angles and an Included Side are known;
solve for the angle opposite the known side using the formula below.
Geometry:
The sum of the angles of a triangle equals 180 degrees.
The sum of the angles of a quadrilateral equals 360 degrees.
A quadrilateral inscribed in a circle has opposite pairs of supplementary angles.

Known: Two Angles,
Side Opposite Angle

[Index]


Entries:
Circle Conversions:
Select the known circle data from the menu, enter the value,
and click on a button to convert.
Angle Unit Conversions:
Select the current angular unit from the menu, enter the value,
and click on a button to convert. Enter a value for the radius
to convert an angle to an arc length.
Angle Conversion Factors:
Pi radians = 180 degrees = 200 grads
Circular Sector
and Segment Calculator:
Select the sector angle or arc length from the menu and enter the value.
Enter the circle radius.
Returns:
Arc:
Portion of the circle circumference. Defined in angular units or length.
Chord:
The line segment connecting the endpoints of an arc.
Center to Chord:
Distance from the center of the circle to the midpoint of the chord.
Sector Area:
The area of the circle bounded by two radii and an arc.
Segment Area:
The area of the circle bounded by the chord and the arc.

Circle Unit Conversion

[Index]

Angle Unit Conversion

[Index]

Circular Sector
and Segment Calculator

[Index]

