Trigonometric Triangle Calculator
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Trigonometric Triangle Calculator
Results
Enter values to calculate.
Understanding Trigonometric Triangle Calculations
Trigonometry is a branch of mathematics that studies relationships between sides and angles of triangles. This calculator helps solve for unknown sides and angles of a triangle when certain information is provided, typically using the Law of Sines or the Law of Cosines.
Right Triangles vs. General Triangles
While basic trigonometry often starts with right triangles (where one angle is 90 degrees), this calculator is designed for general triangles, meaning it can handle any triangle type (acute, obtuse, or right) provided you input enough valid information.
Key Laws Used
-
Law of Cosines: This law relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides
a, b, c and opposite angles A, B, C respectively:
c² = a² + b² - 2ab * cos(C)a² = b² + c² - 2bc * cos(A)b² = a² + c² - 2ac * cos(B)
This law is particularly useful when you know two sides and the included angle (SAS), or when you know all three sides (SSS).
-
Law of Sines: This law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.
a / sin(A) = b / sin(B) = c / sin(C)
This law is useful when you know two angles and one side (AAS or ASA), or when you know two sides and an angle opposite one of them (SSA – though this case can sometimes lead to ambiguous results).
How This Calculator Works
This calculator uses the provided inputs (two sides and the angle opposite one of them, or two sides and the included angle if you were to modify it for that) to calculate the remaining properties of the triangle. Specifically, with two sides (sideA, sideB) and the angle opposite one of them (angleC), it can solve for the remaining side and angles using a combination of the Law of Sines and Law of Cosines. The calculator automatically handles conversions between degrees and radians as selected by the user.
Use Cases
Trigonometric triangle calculations are fundamental in various fields:
- Surveying: Determining distances and elevations.
- Navigation: Calculating positions and courses.
- Engineering: Designing structures and analyzing forces.
- Physics: Solving problems involving vectors and projectile motion.
- Astronomy: Measuring distances to celestial objects.
- Computer Graphics: Rendering 3D scenes and animations.
By inputting known values, you can quickly find missing dimensions or angles, streamlining complex calculations.
function calculateTriangle() {
var sideA = parseFloat(document.getElementById("sideA").value);
var sideB = parseFloat(document.getElementById("sideB").value);
var angleC_deg = parseFloat(document.getElementById("angleC").value);
var angleUnit = document.getElementById("angleUnit").value;
var resultDiv = document.getElementById("calculationResult");
resultDiv.innerHTML = "Calculating…";
// — Input Validation —
if (isNaN(sideA) || isNaN(sideB) || isNaN(angleC_deg)) {
resultDiv.innerHTML = "Error: Please enter valid numbers for all inputs.";
return;
}
if (sideA <= 0 || sideB <= 0) {
resultDiv.innerHTML = "Error: Side lengths must be positive.";
return;
}
if (angleC_deg = 180) {
resultDiv.innerHTML = "Error: Angle C must be between 0 and 180 degrees.";
return;
}
// — Angle Conversion —
var angleC_rad;
if (angleUnit === "degrees") {
angleC_rad = angleC_deg * (Math.PI / 180);
} else {
angleC_rad = angleC_deg; // Assume it's already in radians
if (angleC_rad = Math.PI) {
resultDiv.innerHTML = "Error: Angle C in radians must be between 0 and PI.";
return;
}
}
// — Calculation Logic (Using Law of Cosines to find side c) —
var sideC_squared = Math.pow(sideA, 2) + Math.pow(sideB, 2) – 2 * sideA * sideB * Math.cos(angleC_rad);
if (sideC_squared 1) sinA = 1;
if (sinA < -1) sinA = -1;
var angleA_rad = Math.asin(sinA);
var angleB_rad = Math.PI – angleC_rad – angleA_rad; // Sum of angles in a triangle is PI radians (180 degrees)
// Convert angles back to degrees for display if needed
var angleA_deg = angleA_rad * (180 / Math.PI);
var angleB_deg = angleB_rad * (180 / Math.PI);
// Adjust for potential obtuse angle B if angle A was calculated as acute
// This is a simplification; a full SSA solver is more complex.
// Given SAS (sideA, sideB, angleC), the solution is unique.
// If the input was SSA (e.g., sideA, sideB, angleA), ambiguity could arise.
// Our current input is SAS, so angleA and angleB should be uniquely determined.
var resultHTML = "";
resultHTML += "
Side c: " + sideC.toFixed(4) + " units";
resultHTML += "
Angle A: " + angleA_deg.toFixed(4) + " degrees";
resultHTML += "
Angle B: " + angleB_deg.toFixed(4) + " degrees";
// Verify sum of angles
var angleSum = angleA_deg + angleB_deg + angleC_deg;
if (Math.abs(angleSum – 180) > 0.01) { // Allow for small floating point errors
resultHTML += "
(Note: Angle sum is approximately " + angleSum.toFixed(2) + " degrees due to calculation precision.)";
}
resultDiv.innerHTML = resultHTML;
}