function updateFields(){var mode=document.getElementById('calc_mode').value;var rA=document.getElementById('row_a');var rB=document.getElementById('row_b');var rC=document.getElementById('row_c');var rAngleA=document.getElementById('row_angleA');var rAngleB=document.getElementById('row_angleB');var rAngleC=document.getElementById('row_angleC');rA.style.display='none';rB.style.display='none';rC.style.display='none';rAngleA.style.display='none';rAngleB.style.display='none';rAngleC.style.display='none';if(mode==='sss'){rA.style.display='table-row';rB.style.display='table-row';rC.style.display='table-row';}else if(mode==='sas'){rA.style.display='table-row';rB.style.display='table-row';rAngleC.style.display='table-row';}else if(mode==='asa'){rAngleA.style.display='table-row';rC.style.display='table-row';rAngleB.style.display='table-row';}else if(mode==='aas'){rAngleA.style.display='table-row';rAngleB.style.display='table-row';rA.style.display='table-row';}}function calculateTriangle(){var mode=document.getElementById('calc_mode').value;var a=parseFloat(document.getElementById('side_a').value);var b=parseFloat(document.getElementById('side_b').value);var c=parseFloat(document.getElementById('side_c').value);var A_deg=parseFloat(document.getElementById('angle_A').value);var B_deg=parseFloat(document.getElementById('angle_B').value);var C_deg=parseFloat(document.getElementById('angle_C').value);var resA,resB,resC,steps="";var toDeg=180/Math.PI;var toRad=Math.PI/180;if(mode==='sss'){if(isNaN(a)||isNaN(b)||isNaN(c)){alert('Enter all 3 sides');return;}if(a+b<=c||a+c<=b||b+c=180){alert('Angle must be less than 180°');return;}var c_side=Math.sqrt(a*a+b*b-2*a*b*Math.cos(C_deg*toRad));resA=Math.acos((b*b+c_side*c_side-a*a)/(2*b*c_side))*toDeg;resB=180-C_deg-resA;resC=C_deg;steps="Found side c using Law of Cosines, then calculated remaining angles.";}else if(mode==='asa'){if(isNaN(A_deg)||isNaN(B_deg)||isNaN(c)){alert('Enter angles A, B and side c');return;}if(A_deg+B_deg>=180){alert('Sum of angles must be less than 180°');return;}resC=180-A_deg-B_deg;resA=A_deg;resB=B_deg;steps="Angle C = 180 – (A + B).";}else if(mode==='aas'){if(isNaN(A_deg)||isNaN(B_deg)||isNaN(a)){alert('Enter angles A, B and side a');return;}if(A_deg+B_deg>=180){alert('Sum of angles must be less than 180°');return;}resC=180-A_deg-B_deg;resA=A_deg;resB=B_deg;steps="Angle C = 180 – (A + B).";}document.getElementById('resA').innerHTML=resA.toFixed(2);document.getElementById('resB').innerHTML=resB.toFixed(2);document.getElementById('resC').innerHTML=resC.toFixed(2);if(document.getElementById('show_steps').checked){document.getElementById('stepOutput').innerHTML=steps;document.getElementById('stepOutput').style.display='block';}else{document.getElementById('stepOutput').style.display='none';}document.getElementById('answer').style.display='block';}function resetForm(){document.getElementById('answer').style.display='none';}
Using the Triangle Angle Calculator
A triangle angle calculator is an essential tool for students, engineers, and woodworkers. This tool solves for missing interior angles and side lengths of any triangle based on the information you already have. Whether you are dealing with a right triangle, an isosceles triangle, or a scalene triangle, the geometric principles remain constant: the sum of all internal angles must equal exactly 180 degrees.
To use the calculator, first select the "Calculation Method" from the dropdown. This depends on which parts of the triangle you currently know:
- SSS (Three Sides)
- Enter the lengths of all three sides (a, b, and c). The calculator will use the Law of Cosines to find all three interior angles.
- SAS (Side-Angle-Side)
- Enter two side lengths and the angle situated between them. This is common in land surveying and navigation.
- ASA / AAS (Angle-Side-Angle)
- Enter two known angles and one side length. Since the sum is 180, finding the third angle is the first and easiest step.
How the Triangle Angle Calculator Works
The math behind a triangle angle calculator relies on two fundamental trigonometric laws. Depending on the input, the calculator chooses the most efficient path to the solution.
1. The Law of Cosines
When all three sides are known, we use the Law of Cosines to find an angle:
cos(A) = (b² + c² – a²) / 2bc
Once one angle is found, we can repeat the process for the second, or use the Law of Sines for a faster result.
2. The Triangle Sum Theorem
This is the simplest rule in Euclidean geometry. For any flat triangle:
A + B + C = 180°
Calculation Example: SSS Triangle
Scenario: You have a triangle with side lengths a = 5, b = 6, and c = 7. You need to find Angle A.
Step-by-step solution:
- Identify sides: a=5, b=6, c=7.
- Apply Law of Cosines: cos(A) = (6² + 7² – 5²) / (2 * 6 * 7)
- Calculate: cos(A) = (36 + 49 – 25) / 84
- Calculate: cos(A) = 60 / 84 ≈ 0.7143
- Inverse Cosine: A = arccos(0.7143) ≈ 44.42°
- Result: Angle A is 44.42°.
Common Questions
Can a triangle have two obtuse angles?
No. Since an obtuse angle is greater than 90°, two obtuse angles would total more than 180°, which is impossible for a triangle on a flat plane. Every triangle must have at least two acute angles.
What is the "Ambiguous Case" (SSA)?
The SSA (Side-Side-Angle) configuration is called ambiguous because, depending on the lengths, it can result in zero, one, or two possible triangles. Our triangle angle calculator focuses on the standard configurations (SSS, SAS, ASA) to ensure unique and accurate results.
How do you find the angles of a right triangle?
In a right triangle, one angle is always 90°. You can use basic trigonometry (SOH CAH TOA) such as sin(θ) = opposite/hypotenuse to find the other two angles quickly, or simply use the SAS/SSS modes in this calculator.