Find the Missing Side of a Triangle Calculator

by

Right Triangle Missing Side Calculator

Use this calculator to find the length of an unknown side of a right-angled triangle using the Pythagorean theorem (a² + b² = c²). Enter the lengths of the two known sides and specify what type of sides they are (legs or hypotenuse).

Leg A and Leg B (Find Hypotenuse C) Leg A and Hypotenuse C (Find Leg B) Leg B and Hypotenuse C (Find Leg A)

Result:

Understanding the Right Triangle and Pythagorean Theorem

A right-angled triangle is a special type of triangle where one of its angles measures exactly 90 degrees. The sides of a right triangle have specific names:

  • Legs (a and b): These are the two sides that form the right angle.
  • Hypotenuse (c): This is the longest side of the right triangle and is always opposite the right angle.

The relationship between the sides of a right-angled triangle is described by the famous Pythagorean Theorem, which states: a² + b² = c².

Where:

  • a is the length of one leg.
  • b is the length of the other leg.
  • c is the length of the hypotenuse.

How to Use the Missing Side Calculator

Our calculator simplifies finding any missing side of a right triangle. Here's how it works:

  1. Enter Known Side 1 Length: Input the numerical value of the first side you know.
  2. Enter Known Side 2 Length: Input the numerical value of the second side you know.
  3. Select Side Type: Choose from the dropdown menu to specify what kind of sides you've entered and which side you want to find:
    • "Leg A and Leg B (Find Hypotenuse C)": Use this if you know both legs and want to find the hypotenuse.
    • "Leg A and Hypotenuse C (Find Leg B)": Use this if you know one leg and the hypotenuse, and want to find the other leg.
    • "Leg B and Hypotenuse C (Find Leg A)": Similar to the above, but for finding the other leg.
  4. Click "Calculate Missing Side": The calculator will instantly display the length of the unknown side.

Examples of Finding Missing Sides

Example 1: Finding the Hypotenuse

Imagine you have a right triangle where Leg A is 3 units long and Leg B is 4 units long. You want to find the hypotenuse (c).

  • Known Side 1 (Leg A): 3
  • Known Side 2 (Leg B): 4
  • Side Type: "Leg A and Leg B (Find Hypotenuse C)"

Using the formula: c² = 3² + 4² = 9 + 16 = 25. So, c = √25 = 5. The calculator will output 5.00.

Example 2: Finding a Leg

Suppose you know one leg (Leg A) is 5 units and the hypotenuse (C) is 13 units. You need to find the other leg (Leg B).

  • Known Side 1 (Leg A): 5
  • Known Side 2 (Hypotenuse C): 13
  • Side Type: "Leg A and Hypotenuse C (Find Leg B)"

Using the formula: b² = c² - a² = 13² - 5² = 169 - 25 = 144. So, b = √144 = 12. The calculator will output 12.00.

This calculator is a handy tool for students, engineers, carpenters, and anyone who frequently works with right-angled triangles.

.calculator-container { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; background-color: #f9f9f9; padding: 20px; border-radius: 8px; box-shadow: 0 2px 10px rgba(0,0,0,0.1); max-width: 700px; margin: 20px auto; border: 1px solid #ddd; } .calculator-container h2 { color: #333; text-align: center; margin-bottom: 20px; font-size: 1.8em; } .calculator-container p { color: #555; line-height: 1.6; margin-bottom: 15px; } .calculator-form { background-color: #ffffff; padding: 25px; border-radius: 8px; border: 1px solid #eee; margin-bottom: 30px; } .form-group { margin-bottom: 15px; } .form-group label { display: block; margin-bottom: 8px; color: #333; font-weight: bold; } .form-group input[type="number"], .form-group select { width: calc(100% – 22px); padding: 10px; border: 1px solid #ccc; border-radius: 4px; font-size: 1em; box-sizing: border-box; } button { background-color: #007bff; color: white; padding: 12px 20px; border: none; border-radius: 4px; cursor: pointer; font-size: 1.1em; width: 100%; display: block; margin-top: 20px; transition: background-color 0.3s ease; } button:hover { background-color: #0056b3; } .result-container { background-color: #e9f7ef; border: 1px solid #d4edda; border-radius: 4px; padding: 15px; margin-top: 25px; text-align: center; } .result-container h3 { color: #28a745; margin-top: 0; font-size: 1.4em; } #result { font-size: 1.6em; color: #007bff; font-weight: bold; } .calculator-article { margin-top: 30px; padding: 20px; background-color: #ffffff; border-radius: 8px; border: 1px solid #eee; } .calculator-article h2 { color: #333; font-size: 1.6em; margin-bottom: 15px; border-bottom: 2px solid #eee; padding-bottom: 10px; } .calculator-article h3 { color: #007bff; font-size: 1.3em; margin-top: 20px; margin-bottom: 10px; } .calculator-article ul { list-style-type: disc; margin-left: 20px; margin-bottom: 15px; color: #555; } .calculator-article ol { list-style-type: decimal; margin-left: 20px; margin-bottom: 15px; color: #555; } .calculator-article li { margin-bottom: 8px; } .calculator-article code { background-color: #e0e0e0; padding: 2px 4px; border-radius: 3px; font-family: 'Courier New', Courier, monospace; } function calculateMissingSide() { var knownSide1 = parseFloat(document.getElementById('knownSide1').value); var knownSide2 = parseFloat(document.getElementById('knownSide2').value); var sideType = document.getElementById('sideType').value; var resultDiv = document.getElementById('result'); var missingSide; // Input validation if (isNaN(knownSide1) || isNaN(knownSide2) || knownSide1 <= 0 || knownSide2 <= 0) { resultDiv.innerHTML = "Please enter valid positive numbers for both known sides."; resultDiv.style.color = "red"; return; } resultDiv.style.color = "#007bff"; // Reset color for valid results switch (sideType) { case 'leg_leg': // Known are Leg A and Leg B, find Hypotenuse C missingSide = Math.sqrt(knownSide1 * knownSide1 + knownSide2 * knownSide2); resultDiv.innerHTML = "The Hypotenuse (C) is: " + missingSide.toFixed(2); break; case 'leg_hyp': // Known are Leg A and Hypotenuse C, find Leg B // knownSide1 is Leg A, knownSide2 is Hypotenuse C if (knownSide2 <= knownSide1) { resultDiv.innerHTML = "Error: Hypotenuse (Known Side 2) must be longer than Leg A (Known Side 1)."; resultDiv.style.color = "red"; return; } missingSide = Math.sqrt(knownSide2 * knownSide2 – knownSide1 * knownSide1); resultDiv.innerHTML = "The Missing Leg (B) is: " + missingSide.toFixed(2); break; case 'leg_hyp_reversed': // Known are Leg B and Hypotenuse C, find Leg A // knownSide1 is Leg B, knownSide2 is Hypotenuse C if (knownSide2 <= knownSide1) { resultDiv.innerHTML = "Error: Hypotenuse (Known Side 2) must be longer than Leg B (Known Side 1)."; resultDiv.style.color = "red"; return; } missingSide = Math.sqrt(knownSide2 * knownSide2 – knownSide1 * knownSide1); resultDiv.innerHTML = "The Missing Leg (A) is: " + missingSide.toFixed(2); break; default: resultDiv.innerHTML = "Please select a valid option for known sides."; resultDiv.style.color = "red"; break; } }

Leave a Comment