Obtuse Triangle Calculator

How to use the obtuse triangle calculator

What this calculator does

This calculator performs two related geometry tasks. First, it classifies a triangle from one, two, or three known angles. A complete triangle is obtuse when exactly one interior angle is greater than 90°. Second, it calculates area from one of four standard measurement sets: base and perpendicular height, three sides (SSS), two sides with their included angle (SAS), or two angles with the side between them (ASA). The classification and area sections are deliberately independent, so you can check one triangle's angles while testing an area formula from another measurement set. The result is a mathematical estimate based on the values entered; it does not verify a physical drawing, surveying setup, or measurement accuracy.

When to use it

Use the calculator to check homework or design calculations, confirm whether measured angles describe an obtuse triangle, compare area methods when different measurements are available, or prepare a transparent calculation record for a worksheet. The formulas follow standard plane-triangle identities described in the OpenStax overview of area formulas.

How to calculate

1. The calculator opens with a ready-to-use example: Angle α = 110°, Angle β = 40°, Angle γ = 30°, Base = 12, and Height = 5. Its results are already calculated, and the example Excel workbook is immediately available.
2. Replace one, two, or all three classification angles. With two valid angles, the missing angle is derived. With only one angle, a value above 90° proves the triangle is obtuse, a value of 90° proves it is right, and a smaller value is not enough to classify the entire triangle.
3. Choose a value under Given, then complete the active area fields. Results update live. Read the classification, largest angle, angle sum, area, formula, and the calculation-detail table.
4. Select Download Excel to export the current validated inputs and outputs to a real workbook. Reset clears the demonstration and all measurement fields; Excel export stays disabled until a complete valid state is entered again.

Input guide

Angle α, Angle β, and Angle γ are optional decimal degree values, each greater than 0° and less than 180°. Enter at least one. Examples are 110, 40, and 30. A higher angle can change the classification to right or obtuse; three entered angles must total 180° within 0.01°. Use a period as the decimal separator. Do not enter degree symbols, scientific notation, or decimal commas.

Given selects the area method. Base and Height are required positive lengths in base-height mode; the height must be perpendicular to the base. Example values 12 and 5 produce 30 square units. Side a, Side b, and Side c are required positive lengths in SSS mode and must satisfy the triangle inequality; 7, 9, and 12 are valid. A common error is entering three lengths where one is equal to or longer than the sum of the other two.

In SAS mode, Side a, Side b, and Included angle are required. The angle must lie between the two entered sides, not opposite one of them; 8, 11, and 120° are a realistic example. Increasing either side scales area proportionally, while the angle affects area through its sine. In ASA mode, Angle A, Angle B, and Included side c are required. The two angles must total less than 180°, and side c must join their vertices. For example, 35°, 45°, and 10 units form a valid ASA input. Keep all length entries in the same unit; the output is in the corresponding square unit.

Output guide

Triangle classification reports obtuse, right, acute, or inconclusive. It is exact for a complete valid angle set and a logical conclusion for a single known angle of at least 90°. Largest angle is the maximum provided or derived angle. Angle sum is 180° when two angles determine the third or when three entered angles validate; it is “Not determined” for a one-angle input. Area is a nonnegative estimate in square units driven only by the selected area method. Formula used identifies the identity applied. The detail table lists each angle, whether it was provided or derived, the validated sum, largest angle, and area method.

Worked example

The opening angles are 110°, 40°, and 30°. Their sum is 180°, and the largest is 110°, which is greater than 90°, so the calculator reports Obtuse triangle. With Base = 12 and Height = 5, the area is 0.5 × 12 × 5 = 30.000 square units. These same values appear in the live results, calculation table, and startup Excel workbook. For the SSS method, the calculator instead uses Heron's formula and the semiperimeter.