Obtuse Triangle Calculator

Calculate angles, area, perimeter, altitudes, radii, and classification based on three side lengths. Obtuse Triangle Calculator helps students, engineers, architects, and designers analyze triangles and verify geometric measurements.

Highlights

  • Classifies triangles as obtuse, acute, right, or invalid.
  • Calculates all three interior angles and identifies the largest angle.
  • Finds area, perimeter, and semiperimeter from three side lengths.
  • Determines altitudes corresponding to each triangle side.
  • Calculates the inradius and circumradius in multiple units.

Table of Contents

  1. How Obtuse Triangle Calculator Works?
  2. Practical Use Cases
  3. Accuracy and Limitations
  4. Quick Examples
  5. Frequently Asked Questions (FAQs)
  6. Cite This Calculator

How Obtuse Triangle Calculator Works?

The calculator uses three side lengths, a, b, and c, to determine whether a valid triangle is obtuse, acute, right, or invalid. The side lengths must satisfy the triangle inequality: the sum of any two sides must be greater than the third side.

a+b>c,a+c>b,b+c>a

After validity is confirmed, the perimeter and semiperimeter are calculated by adding the side lengths and taking half of the perimeter.

P=a+b+c,s=P2

The area is found with Heron’s formula, which uses only the three side lengths.

K=s(s−a)(s−b)(s−c)

Each interior angle is calculated with the Law of Cosines. The angle opposite side a, for example, is obtained from the relationship below; the formulas for angles B and C follow the same pattern.

A=cos−1b2+c2−a22bc

The largest angle is opposite the longest side. Therefore, if the longest side is c, the triangle is obtuse when c2 is greater than a2 + b2; it is right when the values are equal and acute when the longest-side square is smaller.

c2>a2+b2⇒C>90°

Altitudes are calculated from the area relationship K = ½ah. Thus, the altitude to each side is twice the area divided by that side. The inradius is the area divided by the semiperimeter, while the circumradius uses all three sides and the area.

ha=2Ka,hb=2Kb,hc=2Kc
r=Ks,R=abc4K

OutputCalculation
PerimeterP = a + b + c
Semiperimeters = P/2
AreaHeron’s formula
AnglesLaw of Cosines
Altitudes2K/a, 2K/b, and 2K/c
InradiusK/s
Circumradiusabc/(4K)

Practical Use Cases

Students: Students can enter three known side lengths to check triangle classification, verify Law of Cosines exercises, calculate all three angles, and compare Heron’s formula with a diagram-based area solution.

Engineers: Engineers can use the calculator to estimate the perimeter, area, altitudes, inradius, and circumradius of triangular components during geometry checks and preliminary structural layouts.

Architects: Architects can analyze triangular floor plans, façades, roof sections, and site boundaries by entering the three measured sides and reviewing the resulting angles and surface area.

Designers: Product and graphic designers can determine the proportions of triangular panels, frames, or decorative elements and use the angle and altitude outputs to support accurate placement and fabrication planning.

Surveyors and field technicians: Surveyors can use three measured side lengths to classify a triangular plot or reference region and quickly obtain its perimeter, area, and associated radii for preliminary documentation.

Accuracy and Limitations

The calculator applies exact geometric formulas—Heron’s formula, the Law of Cosines, altitude-area relationships, and the standard inradius and circumradius equations—then displays rounded numerical results. Inputs must be positive and must satisfy the triangle inequality; otherwise, the triangle is invalid and its geometric outputs cannot be trusted. Classification depends on comparing the square of the longest side with the sum of the squares of the other two sides, so values extremely close to the right-triangle boundary may be affected by input rounding and floating-point precision. Very thin or nearly degenerate triangles can also produce reduced numerical reliability because Heron’s formula involves subtracting nearly equal quantities, and the circumradius becomes very large as the area approaches zero.

Quick Examples

Example #1: Compact Obtuse Triangle

Analyze a small obtuse triangle using centimeter measurements.

Example #2: Large Obtuse Triangle

Calculate geometric properties for an obtuse triangle with dimensions in meters.

Example #3: Imperial Survey Triangle

Evaluate an obtuse triangle from field measurements recorded in feet.

Frequently Asked Questions

An obtuse triangle has one interior angle greater than 90° but less than 180°. Its other two angles must both be acute.

The square of the longest side must be greater than the sum of the squares of the other two sides. The side lengths must also satisfy the triangle inequality.

No. The interior angles of a triangle add up to 180°, so only one angle can be greater than 90°.

The longest side is always opposite the obtuse angle. A larger angle is always opposite a longer side.

Obtuse triangles appear in structural layouts, surveying, architecture, computer graphics, and design whenever three points or edges form a wide-angle shape.

Cite This Calculator