OwlCalculator
OwlCalculator
  • Conversions
  • Health
  • finance Finance Calculator
  • Statistics
  • Combinatorics
  • Percentage Calculators
  • Arithmetic
  • math-curve Algebra
  • Geometry
  • Physics
  • Chemistry

Triangle Side Calculator: Find the Unknown Side of a Triangle

Side

In geometry, a side can be defined as a line connecting two vertices of a figure or two-dimensional figure. Our online calculator will help you find the side, edge of more than 11 shapes.

Triangle

Triangle — is a geometric figure that has three points that do not lie on the same line and three segments that pair these points in pairs. The points of a triangle are usually called its vertices, and the segments are called its sides.

Triangle side calculator

If you need to find the length of one of the sides of a triangle, our free online triangle side calculator can help. Simply select the type and method that suits to your triangle, input the required values, and our calculator will automatically find the length of the unknown side.

Triangle Side Formulas

There are several formulas that you can use to calculate the length of a side of a triangle.

Through two sides and the angle

The cosine theorem in an arbitrary triangle states that one can find a side in a triangle, knowing the other two sides and the angle between them. In order to calculate the third side of the triangle, you need to extract the square root of the difference from the squares of the known sides of their double product by the cosine of the angle between them. The formula is:

b = \sqrt{a^2 + c^2 - 2ac* cos(\alpha)}

where a, b, and c are the lengths of the sides of the triangle, and α is the angle between sides a and c.

You can rearrange the formula to solve for any of the sides. For example, to solve for side c, the formula becomes:

c = \sqrt{a^2 + b^2 - 2ab* cos(\beta)}

Isosceles triangle, through side and angle

Knowing the lateral side of the isosceles triangle and the angle at the base, you can find the third side. To do this, draw a height falling on the base, which will divide the isosceles triangle into two identical right-angled triangles, and the base also into two equal parts. Half of the base from trigonometric relations in the new triangle will be equal to the product of the side (hypotenuse) and the cosine of the angle at the base. The formula is:

b = 2acos(\alpha)

where a, and b are the lengths of the sides of the triangle, and α is the angle between sides a and b.

You can rearrange the formula to solve for side a. The formula becomes:

a = \dfrac{b}{2cos(\alpha)}

Right triangle, through sides

In a right triangle, the side can be found using the Pythagorean theorem. The formula is:

b = \sqrt{a^2+c^2}

where a, b and c are the lengths of the sides of the triangle, b is also known as the hypotenuse.

You can rearrange the formula to solve for any of the sides. For example, to solve for side c, the formula becomes:

c = \sqrt{b^2 - a^2}

Equilateral triangle side, through height

In an equilateral triangle, as well as in the isosceles, the side can be found through height. The formula is:

a = \dfrac{2}{\sqrt{3}}h

where a is the length of the sides of the triangle, and h is the height.

Example Problems

Here are some examples of how to use the formulas to find the length of a side of a triangle.

Example 1

Find the length of side c in a triangle where a = 3, b = 4, and angle α = 90°.

We can use the Law of Cosines to solve for c:

c = \sqrt{a^2 + b^2 - 2ab* cos(\alpha)}

c = \sqrt{3^2 + 4^2 - 2*3*4* cos(90^0)}

c = 5

Therefore, the length of side c is 5 units.

Example 2

Find the length of side b in a right triangle where a = 4, c = 5.

b = \sqrt{a^2+c^2}

b = \sqrt{4^2+5^2}

b = 6.4

Therefore, the length of side b is 6.4 units.

Use our free online calculator to find the length of the unknown side of a triangle. Simply enter the required parameters, and our calculator will automatically find the length of the unknown side.

Using our calculator can save you time and prevent calculation errors. Try it out today!

Follow Us

Tags

triangle side triangle side calculator triangle side formula
  • Area
  • Volume
  • Perimeter
  • Side
  • Height
  • Diagonal
  • Radius
  • Median
  • Bisector
  • Angle
  • Theorems
  • Triangle area
  • Square Area
  • Rectangle Area
  • Circle Area
  • Rhombus Area
  • Parallelogram Area
  • Trapezoid Area Calculator
  • Ellipse Area
  • Annulus Area
  • Quadrilateral Area
  • Annulus Sector Area
  • Circle Sector Area
  • Circle Segment Area
  • Sphere area
  • Cube Area
  • Cylinder area
  • Pyramid area
  • Parallelepiped area
  • Cone area
  • Truncated cone area
  • Tetrahedron area
  • Regular polygon area
  • Sphere volume
  • Cube volume
  • Cylinder volume
  • Pyramid volume
  • Parallelepiped volume
  • Cone volume
  • Truncated cone volume
  • Tetrahedron volume
  • Prism volume
  • Octahedron volume
  • Truncated pyramid volume
  • Ellipsoid volume
  • Capsule volume
  • Hemisphere volume
  • Spherical segment volume
  • Triangle perimeter
  • Square perimeter
  • Rectangle perimeter
  • Circle perimeter
  • Rhombus perimeter
  • Parallelogram perimeter
  • Trapezoid perimeter
  • Ellipse perimeter
  • Annulus perimeter
  • Quadrilateral perimeter
  • Circle sector perimeter
  • Regular polygon perimeter
  • Triangle side calculator
  • Square side calculator
  • Rectangle side calculator
  • Rhombus side calculator
  • Parallelogram side calculator
  • Trapezoid side calculator
  • Cube side calculator
  • Parallelepiped side calculator
  • Pyramid side calculator
  • Tetrahedron side calculator
  • Triangle height calculator
  • Trapezoid height calculator
  • Parallelogram/Rhombus height calculator
  • Pyramid height calculator
  • Prism height calculator
  • Cylinder height calculator
  • Cone height calculator
  • Square diagonal calculator
  • Rectangle diagonal calculator
  • Rhombus diagonal calculator
  • Parallelogram diagonal calculator
  • Trapezoid diagonal calculator
  • Cube diagonal calculator
  • Parallelepiped diagonal calculator
  • Cylinder diagonal calculator
  • Circle radius calculator
  • Cylinder radius calculator
  • Sphere radius calculator
  • Triangle median calculator
  • Triangle bisector calculator
  • Parallelogram bisector calculator
  • Trapezoid bisector calculator
  • Triangle angles
  • Rhombus angles
  • Sine of angle
  • Cosine of angle
  • Tangent of angle
  • Cotangent of angle
  • Pythagorean theorem
  • Sinus theorem
  • Cosine theorem
  • Tangens theorem
  • Cotangent theorem
  • Tangent-Secant theorem

OwlCalculator

2019-2025

Information F.A.Q About Us Terms of Service Privacy Policy Contact Us
Follow Us

© Copyright by iForce Systems LLC