Area of an Obtuse Triangle Calculator
Calculate the area, third side, perimeter, and altitude based on two adjacent sides and their included obtuse angle. Area of an Obtuse Triangle Calculator helps students, engineers, architects, and educators solve geometric measurements efficiently.
Highlights
- Calculate the area of an obtuse triangle using two sides and the included angle.
- Determine the unknown third side with the Law of Cosines.
- Find the triangle’s perimeter from all three side lengths.
- Calculate the altitude relative to the first side.
- Supports multiple length and area units, including metric and imperial measurements.
Table of Contents
How Area of an Obtuse Triangle Calculator Works?
This calculator determines the area and related measurements of a triangle when two adjacent sides and their included angle are known. The included angle must be greater than 90° and less than 180°, which identifies the triangle as obtuse.
The area is calculated with the two-side and included-angle formula:
Here, a is the first side, b is the second side, and θ is the obtuse included angle. Because the sine of an obtuse angle is positive, the area remains positive.
The third side, which is opposite the included angle, is found using the law of cosines:
The perimeter is the sum of the three side lengths:
The altitude measured to the first side follows from the area formula:
For example, using a first side of 5 m, a second side of 7 m, and an included angle of 120°, the calculator produces approximately 15.155 m² for the area, 10.440 m for the third side, 22.440 m for the perimeter, and 6.062 m for the altitude to the first side.
| Output | Mathematical basis |
|---|---|
| Triangle Area | |
| Third Side | |
| Perimeter | |
| Altitude to First Side |
The side inputs accept positive values from 0.000001 to 1,000,000,000 in supported length units including mm, cm, m, km, in, ft, yd, and mi. The angle input accepts values from 90.01° to 179.99°.
Practical Use Cases
Students: Students can verify geometry homework involving obtuse triangles by entering two known sides and the included angle, then comparing the calculated area, opposite side, perimeter, and altitude with their manual work.
Engineers: Engineers can use the calculator for preliminary geometry checks involving triangular components, layouts, or structural members when two connected lengths and their obtuse angle are available.
Architects: Architects can estimate the surface area and boundary length of irregular triangular design features, floor sections, façade elements, or site layouts represented by an obtuse triangle.
Surveyors and site planners: Surveyors and planners can calculate a third distance and enclosed area from two measured lines and the angle between them, supporting early-stage boundary and land-layout assessments.
Educators: Teachers can demonstrate how the sine rule for area and the law of cosines work together, using the calculator to create examples and check classroom calculations.
Accuracy and Limitations
The calculator applies the two-side area formula, the law of cosines, and the altitude relationship using the entered values, with results affected only by the precision of the input data and displayed rounding. Both side lengths must be positive, and the included angle must be between 90.01° and 179.99°; angles outside that range are not accepted. The calculated third side must satisfy the triangle inequality mathematically, which it will for valid positive sides and an included angle strictly between 0° and 180°. The result assumes a flat Euclidean triangle and does not account for measurement errors, curved surfaces, distorted drawings, or uncertainty in field measurements.
Quick Examples
Example #1: Construction Layout
Calculate the area and dimensions of an obtuse triangular section using two sides measured in meters.
Example #2: Architectural Panel
Determine the measurements of an obtuse triangular architectural panel from centimeter-based side lengths.
Example #3: Surveying Plot
Estimate the area, perimeter, and altitude of an obtuse triangular land section using kilometer measurements.
