Right Triangle Missing Side Calculator
Enter the lengths of two sides of a right-angled triangle, and this calculator will find the length of the missing third side using the Pythagorean theorem.
function calculateMissingSide() {
var sideA_str = document.getElementById("sideA").value;
var sideB_str = document.getElementById("sideB").value;
var sideC_str = document.getElementById("sideC").value;
var sideA = parseFloat(sideA_str);
var sideB = parseFloat(sideB_str);
var sideC = parseFloat(sideC_str);
var isAValid = !isNaN(sideA) && sideA > 0;
var isBValid = !isNaN(sideB) && sideB > 0;
var isCValid = !isNaN(sideC) && sideC > 0;
var missingCount = 0;
if (!isAValid) missingCount++;
if (!isBValid) missingCount++;
if (!isCValid) missingCount++;
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (missingCount === 1) {
var calculatedSide;
var sideName;
if (!isAValid) {
// Calculate Leg A
if (!isBValid || !isCValid) {
resultDiv.innerHTML = "Error: Internal logic error. Please report this issue.";
return;
}
if (sideC <= sideB) {
resultDiv.innerHTML = "Error: The hypotenuse (Side C) must be longer than Leg B.";
return;
}
calculatedSide = Math.sqrt(Math.pow(sideC, 2) – Math.pow(sideB, 2));
sideName = "Leg A";
} else if (!isBValid) {
// Calculate Leg B
if (!isAValid || !isCValid) {
resultDiv.innerHTML = "Error: Internal logic error. Please report this issue.";
return;
}
if (sideC <= sideA) {
resultDiv.innerHTML = "Error: The hypotenuse (Side C) must be longer than Leg A.";
return;
}
calculatedSide = Math.sqrt(Math.pow(sideC, 2) – Math.pow(sideA, 2));
sideName = "Leg B";
} else { // !isCValid
// Calculate Hypotenuse C
if (!isAValid || !isBValid) {
resultDiv.innerHTML = "Error: Internal logic error. Please report this issue.";
return;
}
calculatedSide = Math.sqrt(Math.pow(sideA, 2) + Math.pow(sideB, 2));
sideName = "Hypotenuse C";
}
if (isNaN(calculatedSide) || calculatedSide <= 0) {
resultDiv.innerHTML = "Error: Calculation resulted in an invalid length. Please check your inputs (e.g., hypotenuse must be longer than legs).";
} else {
resultDiv.innerHTML = "The missing " + sideName + " is:
" + calculatedSide.toFixed(4) + " units";
}
} else if (missingCount === 0) {
// All sides entered, check if it's a valid right triangle
var pythagoreanCheck = Math.pow(sideA, 2) + Math.pow(sideB, 2);
var hypotenuseSquared = Math.pow(sideC, 2);
// Use a small tolerance for floating point comparison
if (Math.abs(pythagoreanCheck – hypotenuseSquared) < 0.0001) {
resultDiv.innerHTML = "The entered sides (A=" + sideA + ", B=" + sideB + ", C=" + sideC + ") form a valid right-angled triangle.";
} else {
resultDiv.innerHTML = "The entered sides (A=" + sideA + ", B=" + sideB + ", C=" + sideC + ") do NOT form a right-angled triangle according to the Pythagorean theorem (A² + B² ≠ C²).";
}
} else {
resultDiv.innerHTML = "Please enter exactly two side lengths to calculate the missing one.";
}
}
function clearInputs() {
document.getElementById("sideA").value = "";
document.getElementById("sideB").value = "";
document.getElementById("sideC").value = "";
document.getElementById("result").innerHTML = "";
}
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font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
border: 1px solid #ddd;
border-radius: 8px;
padding: 25px;
max-width: 600px;
margin: 30px auto;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.08);
}
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color: #333;
text-align: center;
margin-bottom: 20px;
font-size: 1.8em;
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line-height: 1.6;
margin-bottom: 15px;
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.calculator-inputs label {
display: block;
margin-bottom: 8px;
color: #333;
font-weight: bold;
font-size: 1.1em;
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.calculator-inputs input[type="number"] {
width: calc(100% – 80px); /* Adjust width for unit span */
padding: 12px;
margin-bottom: 10px;
border: 1px solid #ccc;
border-radius: 5px;
box-sizing: border-box;
font-size: 1em;
display: inline-block;
vertical-align: middle;
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.calculator-inputs .input-unit {
display: inline-block;
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width: 60px;
text-align: left;
padding-left: 5px;
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.calculator-inputs .input-hint {
font-size: 0.85em;
color: #777;
margin-top: -5px;
margin-bottom: 15px;
}
.calculator-inputs button {
background-color: #007bff;
color: white;
padding: 12px 20px;
border: none;
border-radius: 5px;
cursor: pointer;
font-size: 1.1em;
margin-right: 10px;
transition: background-color 0.3s ease;
}
.calculator-inputs button:hover {
background-color: #0056b3;
}
.calculator-inputs button:last-child {
background-color: #6c757d;
}
.calculator-inputs button:last-child:hover {
background-color: #5a6268;
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.calculator-result {
margin-top: 25px;
padding: 15px;
border-radius: 5px;
background-color: #e9ecef;
border: 1px solid #dee2e6;
font-size: 1.1em;
color: #333;
text-align: center;
}
.calculator-result p {
margin: 0;
padding: 5px 0;
}
.calculator-result .success {
color: #28a745;
font-weight: bold;
}
.calculator-result .error {
color: #dc3545;
font-weight: bold;
}
.calculator-result .warning {
color: #ffc107;
font-weight: bold;
}
.calculator-result .info {
color: #17a2b8;
font-weight: bold;
}
Understanding the Missing Side of a Right-Angled Triangle
A right-angled triangle is a special type of triangle where one of its angles measures exactly 90 degrees. The side opposite the right angle is called the hypotenuse, and it is always the longest side. The other two sides are called legs.
The Pythagorean Theorem
The relationship between the sides of a right-angled triangle is described by the famous Pythagorean Theorem, named after the ancient Greek mathematician Pythagoras. The theorem states:
a² + b² = c²
Where:
a and b are the lengths of the two legs of the right triangle.c is the length of the hypotenuse.
This theorem is fundamental in geometry and trigonometry and allows us to find the length of any missing side if the other two sides are known.
How to Use the Calculator
Our Missing Side of Right Triangle Calculator simplifies this process for you. Here's how to use it:
- Identify Your Known Sides: Look at your right-angled triangle and determine which two side lengths you already know.
- Enter Values: Input the lengths of the two known sides into their respective fields (Leg A, Leg B, or Hypotenuse C).
- Leave Missing Side Blank: Do NOT enter a value for the side you wish to calculate. The calculator will automatically identify the blank field as the missing side.
- Click "Calculate": Press the "Calculate Missing Side" button.
- View Result: The calculator will display the length of the missing side. If you entered all three sides, it will verify if they form a valid right-angled triangle.
Important Note: The units of the calculated side will be the same as the units you input (e.g., if you enter values in centimeters, the result will be in centimeters).
Examples of Calculating Missing Sides
Example 1: Finding the Hypotenuse
Imagine you have a right-angled triangle where Leg A is 3 units long and Leg B is 4 units long. You want to find the length of the hypotenuse (Side C).
- Enter "3" in the "Leg A" field.
- Enter "4" in the "Leg B" field.
- Leave "Hypotenuse C" blank.
- Click "Calculate".
Result: The calculator will show that Hypotenuse C is 5 units. (3² + 4² = 9 + 16 = 25, and √25 = 5)
Example 2: Finding a Leg
Suppose you know the hypotenuse (Side C) is 13 units long and one leg (Leg A) is 5 units long. You need to find the length of the other leg (Leg B).
- Enter "5" in the "Leg A" field.
- Leave "Leg B" blank.
- Enter "13" in the "Hypotenuse C" field.
- Click "Calculate".
Result: The calculator will determine that Leg B is 12 units. (13² – 5² = 169 – 25 = 144, and √144 = 12)
Example 3: Verifying a Right Triangle
You have a triangle with sides 6, 8, and 10 units. You want to check if it's a right-angled triangle.
- Enter "6" in the "Leg A" field.
- Enter "8" in the "Leg B" field.
- Enter "10" in the "Hypotenuse C" field.
- Click "Calculate".
Result: The calculator will confirm that these sides form a valid right-angled triangle. (6² + 8² = 36 + 64 = 100, and 10² = 100)
This calculator is a handy tool for students, engineers, carpenters, and anyone working with geometric problems involving right-angled triangles.