Triangle Side Length Calculator
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margin: 0;
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.loan-calc-container {
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padding: 30px;
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.input-group input[type="number"] {
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#result-value {
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}
Triangle Side Length Calculator
Calculate the length of a triangle's side using the Pythagorean theorem or the Law of Cosines.
Understanding Triangle Side Length Calculations
Triangles are fundamental geometric shapes with three sides and three angles. Calculating the length of a specific side is a common task in geometry, trigonometry, engineering, and various practical applications. The method used depends on the type of triangle and the information provided.
1. Right Triangles and the Pythagorean Theorem
A right triangle is a triangle that has one angle measuring exactly 90 degrees. The side opposite the right angle is called the hypotenuse (usually denoted as 'c'), and the other two sides are called legs (usually denoted as 'a' and 'b'). The Pythagorean theorem provides a simple and elegant way to find the length of any side if the other two are known.
a² + b² = c²
Where:
- 'a' and 'b' are the lengths of the legs.
- 'c' is the length of the hypotenuse.
This calculator uses the Pythagorean theorem to find an unknown side. If you know the two legs (a and b), you can find the hypotenuse (c) by calculating c = √(a² + b²). If you know one leg (e.g., a) and the hypotenuse (c), you can find the other leg (b) by calculating b = √(c² – a²).
2. General Triangles and the Law of Cosines
For triangles that are not necessarily right-angled (general triangles), the Law of Cosines is used. This law relates the lengths of the sides of a triangle to the cosine of one of its angles. It's a generalization of the Pythagorean theorem.
c² = a² + b² – 2ab cos(γ)
Where:
- 'a', 'b', and 'c' are the lengths of the sides of the triangle.
- 'γ' (gamma) is the angle opposite side 'c'.
This calculator allows you to find the length of side 'c' if you know the lengths of sides 'a' and 'b', and the measure of the angle 'γ' between them. The angle must be provided in degrees.
If you need to find side 'a' or 'b' using the Law of Cosines, the formulas are rearranged:
a² = b² + c² – 2bc cos(α)
b² = a² + c² – 2ac cos(β)
Where 'α' is the angle opposite side 'a', and 'β' is the angle opposite side 'b'.
Use Cases:
- Construction & Architecture: Ensuring structural integrity and accurate measurements for buildings, bridges, and other structures.
- Navigation: Calculating distances and positions using triangulation.
- Engineering: Designing mechanical parts, analyzing forces, and solving spatial problems.
- Surveying: Determining land boundaries and elevations.
- Computer Graphics: Rendering 3D models and calculating object positions.
- Physics: Analyzing vectors, forces, and projectile motion.
function updateInputs() {
var type = document.getElementById("triangleType").value;
if (type === "right") {
document.getElementById("pythagoreanInputs").style.display = "block";
document.getElementById("lawOfCosinesInputs").style.display = "none";
} else {
document.getElementById("pythagoreanInputs").style.display = "none";
document.getElementById("lawOfCosinesInputs").style.display = "block";
}
}
function calculateSideLength() {
var type = document.getElementById("triangleType").value;
var resultValueElement = document.getElementById("result-value");
var resultUnitElement = document.getElementById("result-unit");
resultValueElement.textContent = "–";
resultUnitElement.textContent = "";
if (type === "right") {
var sideA = parseFloat(document.getElementById("sideA").value);
var sideB = parseFloat(document.getElementById("sideB").value);
var knownSide = document.getElementById("knownSide").value;
if (isNaN(sideA) || isNaN(sideB) || sideA <= 0 || sideB = sideA) {
calculatedSide = Math.sqrt(sideB * sideB – sideA * sideA);
sideLabel = "Side A (a)";
} else {
alert("For a right triangle, the hypotenuse must be longer than a leg. Side B cannot be shorter than Side A if Side A is the hypotenuse.");
return;
}
} else if (knownSide === "sideB") {
if (sideA >= sideB) {
calculatedSide = Math.sqrt(sideA * sideA – sideB * sideB);
sideLabel = "Side B (b)";
} else {
alert("For a right triangle, the hypotenuse must be longer than a leg. Side A cannot be shorter than Side B if Side B is the hypotenuse.");
return;
}
}
resultValueElement.textContent = calculatedSide.toFixed(4);
resultUnitElement.textContent = "units";
} else if (type === "general") {
var side1 = parseFloat(document.getElementById("side1").value);
var side2 = parseFloat(document.getElementById("side2").value);
var angleC_deg = parseFloat(document.getElementById("angleC").value);
var knownSideCos = document.getElementById("knownSideCos").value;
if (isNaN(side1) || isNaN(side2) || isNaN(angleC_deg) || side1 <= 0 || side2 <= 0 || angleC_deg = 180) {
alert("Please enter valid positive numbers for Side 1 and Side 2, and an angle between 0 and 180 degrees.");
return;
}
var angleC_rad = angleC_deg * (Math.PI / 180); // Convert degrees to radians
var calculatedSide = 0;
var sideLabel = "";
if (knownSideCos === "side3") {
calculatedSide = Math.sqrt(side1 * side1 + side2 * side2 – 2 * side1 * side2 * Math.cos(angleC_rad));
sideLabel = "Side 3 (c)";
} else if (knownSideCos === "side1") {
// Rearranging Law of Cosines for side 'a' (side1)
// a² = b² + c² – 2bc cos(α)
// We need angle alpha, which is not directly given.
// This calculator is designed to find the side OPPOSITE the given angle.
// If the user selects 'side1' as the known side to find, it implies they want to find 'a'
// but the input angle is 'C'. This scenario is ambiguous without more angles.
// For simplicity and clarity, we'll assume the calculator finds the side opposite the given angle.
// If the user wants to find side 'a', they should input 'b', 'c', and angle 'A'.
// We will provide a message indicating this limitation or ask for more info.
alert("To find Side 1 (a) using the Law of Cosines, you need to know Side 2 (b), Side 3 (c), and Angle A (α). This calculator is set up to find the side opposite the given angle.");
return;
} else if (knownSideCos === "side2") {
// Similar to finding side1, finding side2 requires angle B.
alert("To find Side 2 (b) using the Law of Cosines, you need to know Side 1 (a), Side 3 (c), and Angle B (β). This calculator is set up to find the side opposite the given angle.");
return;
}
resultValueElement.textContent = calculatedSide.toFixed(4);
resultUnitElement.textContent = "units";
}
}
// Initialize the correct input fields on page load
document.addEventListener('DOMContentLoaded', updateInputs);