What Is FREE TOOLS Triangle Calculator?

A Triangle Calculator is a free online tool that helps you calculate important measurements of a triangle, including side lengths, angles, area, perimeter, and height.

Depending on the information provided, the calculator can solve different types of triangles, including right, equilateral, isosceles, and scalene triangles.

What Can a Triangle Calculator Calculate?

A FREE TOOLS Triangle Calculator may calculate:

• Missing side lengths
• Missing angles
• Triangle area
• Perimeter
• Height or altitude
• Semiperimeter
• Internal angles
• Other geometric measurements

It can solve a triangle when enough known measurements are provided.

Common Triangle Formulas

Triangle Area

When the base and height are known: A=12bh\boxed{A=\frac{1}{2}bh}

Where:

• AA = area
• bb = base
• hh = height

For example, if the base is 10 and height is 6: A=12(10)(6)=30A=\frac{1}{2}(10)(6)=30

The area is 30 square units.

Triangle Perimeter

The perimeter is the sum of all three sides: P=a+b+c\boxed{P=a+b+c}

For sides 5, 6, and 7: P=5+6+7=18P=5+6+7=18

So the perimeter is 18 units.

Heron’s Formula

When all three side lengths are known, the area can be calculated using: s=a+b+c2s=\frac{a+b+c}{2}

Then: A=s(s−a)(s−b)(s−c)\boxed{A=\sqrt{s(s-a)(s-b)(s-c)}}

This is particularly useful when the height is not known.

Using Trigonometry

For triangles that are not right triangles, a Triangle Calculator may use the Law of Sines or Law of Cosines.

Law of Sines

asin⁡A=bsin⁡B=csin⁡C\boxed{\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}}

Law of Cosines

c2=a2+b2−2abcos⁡C\boxed{c^2=a^2+b^2-2ab\cos C}

These formulas allow the calculator to determine unknown sides or angles from known triangle measurements.

Example

Suppose a triangle has sides:

• a=5a=5
• b=6b=6
• c=7c=7

The perimeter is: P=5+6+7=18P=5+6+7=18

The semiperimeter is: s=182=9s=\frac{18}{2}=9

Using Heron’s Formula: A=9(9−5)(9−6)(9−7)A=\sqrt{9(9-5)(9-6)(9-7)} A=216A=\sqrt{216} A≈14.697A\approx14.697

Therefore, the triangle has an area of approximately 14.70 square units.

Types of Triangles

A Triangle Calculator can be used with several triangle types:

• Equilateral Triangle – three equal sides and three 60° angles.
• Isosceles Triangle – two equal sides.
• Scalene Triangle – all three sides have different lengths.
• Right Triangle – one angle equals 90°.
• Acute Triangle – all angles are less than 90°.
• Obtuse Triangle – one angle is greater than 90°.

How Does a Triangle Calculator Work?

You enter the measurements you already know, such as:

1. Three side lengths
2. Two sides and an included angle
3. Two angles and one side
4. Base and height
5. Other valid combinations of sides and angles

The calculator then selects the appropriate mathematical formula and calculates the missing values.

Why Use a Triangle Calculator?

A FREE TOOLS Triangle Calculator is useful for:

• Geometry homework
• Trigonometry problems
• Construction measurements
• Architecture
• Engineering
• Surveying
• Land measurement
• Calculating distances and angles
• Checking manual calculations

In Simple Terms

A FREE TOOLS Triangle Calculator is an online tool that makes it easy to solve triangles and calculate their missing measurements.

Depending on the information entered, it can calculate sides, angles, area, perimeter, and height using formulas such as the Pythagorean Theorem, Heron’s Formula, Law of Sines, and Law of Cosines.

It is a convenient tool for students, teachers, engineers, builders, and anyone working with triangle geometry and trigonometry.

Keep working with triangle calculations