Obtuse Triangle Calculator
Solve triangle (sides, angles, area, perimeter) — works for obtuse triangles.
In geometry, not all triangles have right angles. Some triangles have one angle that is greater than 90°, and these are called obtuse triangles. Because of their shape, obtuse triangles behave differently from right or acute triangles, and special formulas are needed to solve them.
The Obtuse Triangle Calculator is designed to help you find missing sides, angles, area, and other properties of an obtuse triangle quickly and accurately. Instead of using long manual calculations, you simply enter the known values, and the calculator applies the correct trigonometric formulas automatically.
This tool is useful for students, teachers, engineers, surveyors, and anyone working with triangle measurements.
What the Obtuse Triangle Calculator Is
A Non‑Right Triangle Solver
The Obtuse Triangle Calculator is an online geometry tool that solves triangles with one angle greater than 90°. These triangles do not follow the Pythagorean Theorem, so the calculator uses more general trigonometric rules.
You can use this calculator when you know:
Two sides and the obtuse angle between them
Two angles and one side
All three sides
The calculator then finds all the missing triangle values.
What the Calculator Can Find
The calculator can compute:
Missing side lengths
Missing angle measures
Triangle area
Triangle perimeter
Sometimes triangle heights
All results are based on standard geometry and trigonometry formulas.
How the Obtuse Triangle Calculator Works
Step 1: Enter Known Values
You begin by entering the triangle measurements you already have, such as side lengths and angle values.
Step 2: Apply Trigonometric Laws
The calculator selects the correct formula:
Law of Cosines for side‑angle‑side problems
Law of Sines for angle‑side relationships
Step 3: Display the Results
The tool instantly shows the missing sides, angles, area, and perimeter.
This process makes solving obtuse triangles fast and accurate.
Key Formulas Used
Triangle Angle Sum Rule
The interior angles of any triangle always add up to 180°.
Law of Cosines
Used when two sides and the included angle are known.
c^2 = a^2 + b^2 - 2ab\cos(C)This formula works even when angle C is obtuse.
Law of Sines
Used when two angles and one side are known.
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}Area Using Two Sides and an Angle
\text{Area} = \frac{1}{2} ab\sin(C)Heron’s Formula (All Sides Known)
s = \frac{a + b + c}{2} \text{Area} = \sqrt{s(s-a)(s-b)(s-c)}Step‑by‑Step Examples
Example 1: Using the Law of Cosines
Given:
a = 9 units
b = 7 units
C = 110°
Find side c.
c^2 = 9^2 + 7^2 - 2(9)(7)\cos(110^\circ) c^2 = 81 + 49 - 126(-0.342) c^2 \approx 173.1 c \approx 13.16 \text{ units}Example 2: Finding a Missing Angle
Given:
A = 35°
B = 45°
Find angle C.
C = 180^\circ - (35^\circ + 45^\circ) C = 100^\circThis triangle is obtuse because one angle is greater than 90°.
Features of the Obtuse Triangle Calculator
Solves All Obtuse Triangles
The calculator works for any triangle with an angle greater than 90°.
Uses Correct Trigonometric Rules
It applies the Law of Cosines and Law of Sines automatically.
Fast and Accurate Results
All calculations are completed instantly.
Simple to Use
Just enter known values and get the results without complex math.
Uses and Applications
Education and Learning
Students use the calculator to solve geometry problems and understand obtuse triangle properties.
Engineering and Construction
Engineers and builders use obtuse triangle calculations for measurements, layouts, and structural planning.
Surveying and Design
Surveyors and designers use triangle geometry to measure land and plan designs accurately.
Tips to Avoid Common Mistakes
Many users try to apply the Pythagorean Theorem to obtuse triangles, but this formula only works for right triangles. Always use the Law of Cosines or Law of Sines for obtuse cases.
Another common mistake is using the wrong angle in the cosine formula. The angle must be the included angle between the two known sides.
Some users forget that triangle angles must add up to 180°. If your angles do not follow this rule, the triangle is invalid.
Using different units for side lengths can also cause incorrect results. Always keep all values in the same unit system.
Finally, avoid rounding too early. Let the calculator complete all calculations before rounding the final answers.
FAQs
What is an obtuse triangle?
It is a triangle with one angle greater than 90°.
Which formulas are used to solve obtuse triangles?
The Law of Cosines and the Law of Sines.
Can this calculator find area and perimeter?
Yes, it calculates both.
Is this calculator free to use?
Most obtuse triangle calculators are free online.
Final Words
The Obtuse Triangle Calculator is a reliable and easy‑to‑use geometry tool for solving non‑right triangles.
Whether you are a student, teacher, engineer, or surveyor, this calculator saves time, improves accuracy, and makes obtuse triangle calculations simple.