Angle Right Triangle Calculator

Right Angle Triangle Calculator

Enter any two values (at least one side) to calculate the rest.






.calculator-container { background-color: #f9f9f9; border: 1px solid #ddd; padding: 20px; border-radius: 8px; max-width: 600px; margin: 20px auto; font-family: Arial, sans-serif; } .calculator-container h2 { text-align: center; color: #333; margin-bottom: 20px; } .calculator-inputs label { display: inline-block; width: 180px; margin-bottom: 10px; font-weight: bold; } .calculator-inputs input[type="number"] { width: calc(100% – 200px); padding: 8px; margin-bottom: 10px; border: 1px solid #ccc; border-radius: 4px; } .calculator-inputs button { background-color: #007bff; color: white; padding: 10px 15px; border: none; border-radius: 4px; cursor: pointer; font-size: 16px; margin-right: 10px; margin-top: 10px; } .calculator-inputs button:hover { background-color: #0056b3; } .calculator-results { margin-top: 20px; padding: 15px; background-color: #e9ecef; border: 1px solid #ced4da; border-radius: 4px; } .calculator-results h3 { color: #333; margin-top: 0; } .calculator-results p { margin: 5px 0; } .error { color: red; font-weight: bold; } function calculateTriangle() { var a = NaN, b = NaN, c = NaN, A_deg = NaN, B_deg = NaN; var PI = Math.PI; // Helper function to convert degrees to radians function toRadians(degrees) { return degrees * (PI / 180); } // Helper function to convert radians to degrees function toDegrees(radians) { return radians * (180 / PI); } // Read inputs var input_a = parseFloat(document.getElementById('sideA').value); var input_b = parseFloat(document.getElementById('sideB').value); var input_c = parseFloat(document.getElementById('hypotenuseC').value); var input_A_deg = parseFloat(document.getElementById('angleA_deg').value); var input_B_deg = parseFloat(document.getElementById('angleB_deg').value); var validInputsCount = 0; if (!isNaN(input_a) && input_a > 0) { a = input_a; validInputsCount++; } if (!isNaN(input_b) && input_b > 0) { b = input_b; validInputsCount++; } if (!isNaN(input_c) && input_c > 0) { c = input_c; validInputsCount++; } if (!isNaN(input_A_deg) && input_A_deg > 0 && input_A_deg 0 && input_B_deg < 90) { B_deg = input_B_deg; validInputsCount++; } var resultHTML = ''; var solved = false; if (validInputsCount = c) { resultHTML = 'Side \'a\' cannot be greater than or equal to hypotenuse \'c\'.'; } else { b = Math.sqrt(c*c – a*a); A_deg = toDegrees(Math.asin(a/c)); B_deg = 90 – A_deg; solved = true; } } else if (!isNaN(b) && !isNaN(c)) { // Case: b, c given if (b >= c) { resultHTML = 'Side \'b\' cannot be greater than or equal to hypotenuse \'c\'.'; } else { a = Math.sqrt(c*c – b*b); B_deg = toDegrees(Math.asin(b/c)); A_deg = 90 – B_deg; solved = true; } } // If not solved by two sides, try one side and one angle if (!solved) { if (!isNaN(a) && !isNaN(A_deg)) { // Case: a, A given var A_rad = toRadians(A_deg); B_deg = 90 – A_deg; c = a / Math.sin(A_rad); b = a / Math.tan(A_rad); solved = true; } else if (!isNaN(a) && !isNaN(B_deg)) { // Case: a, B given var B_rad = toRadians(B_deg); A_deg = 90 – B_deg; c = a / Math.cos(B_rad); b = a * Math.tan(B_rad); solved = true; } else if (!isNaN(b) && !isNaN(A_deg)) { // Case: b, A given var A_rad = toRadians(A_deg); B_deg = 90 – A_deg; c = b / Math.cos(A_rad); a = b * Math.tan(A_rad); solved = true; } else if (!isNaN(b) && !isNaN(B_deg)) { // Case: b, B given var B_rad = toRadians(B_deg); A_deg = 90 – B_deg; c = b / Math.sin(B_rad); a = b / Math.tan(B_rad); solved = true; } else if (!isNaN(c) && !isNaN(A_deg)) { // Case: c, A given var A_rad = toRadians(A_deg); B_deg = 90 – A_deg; a = c * Math.sin(A_rad); b = c * Math.cos(A_rad); solved = true; } else if (!isNaN(c) && !isNaN(B_deg)) { // Case: c, B given var B_rad = toRadians(B_deg); A_deg = 90 – B_deg; a = c * Math.cos(B_rad); b = c * Math.sin(B_rad); solved = true; } } if (solved) { // Calculate Area and Perimeter var area = 0.5 * a * b; var perimeter = a + b + c; resultHTML = '

Calculated Triangle Properties:

'; resultHTML += 'Side a: ' + a.toFixed(4) + "; resultHTML += 'Side b: ' + b.toFixed(4) + "; resultHTML += 'Hypotenuse c: ' + c.toFixed(4) + "; resultHTML += 'Angle A: ' + A_deg.toFixed(4) + ' degrees'; resultHTML += 'Angle B: ' + B_deg.toFixed(4) + ' degrees'; resultHTML += 'Angle C: 90 degrees'; resultHTML += 'Area: ' + area.toFixed(4) + "; resultHTML += 'Perimeter: ' + perimeter.toFixed(4) + "; } else if (resultHTML === ") { // If no specific error message was set, but not solved resultHTML = 'Could not solve the triangle with the given inputs. Please ensure at least one side is provided, and values are consistent.'; } } document.getElementById('triangleResult').innerHTML = resultHTML; } function clearInputs() { document.getElementById('sideA').value = "; document.getElementById('sideB').value = "; document.getElementById('hypotenuseC').value = "; document.getElementById('angleA_deg').value = "; document.getElementById('angleB_deg').value = "; document.getElementById('triangleResult').innerHTML = "; }

Understanding the Right Angle Triangle Calculator

A right angle triangle is a special type of triangle that has one angle exactly equal to 90 degrees. This unique property makes it fundamental in geometry, trigonometry, engineering, and many other fields. Our Right Angle Triangle Calculator helps you quickly find missing sides, angles, area, and perimeter of such a triangle by providing just two pieces of information (at least one of which must be a side).

Key Properties of a Right Angle Triangle

  • Right Angle: One angle (usually denoted as C) measures exactly 90 degrees.
  • Hypotenuse: The side opposite the right angle (denoted as 'c') is always the longest side of the triangle.
  • Legs (or Cathetus): The two sides adjacent to the right angle (denoted as 'a' and 'b') are called legs.
  • Pythagorean Theorem: For any right angle triangle, the square of the hypotenuse (c²) is equal to the sum of the squares of the other two sides (a² + b²). This is expressed as a² + b² = c².
  • Sum of Angles: The sum of all three interior angles in any triangle is 180 degrees. Since one angle is 90 degrees, the sum of the other two acute angles (A and B) must be 90 degrees (A + B = 90°).

Trigonometric Ratios (SOH CAH TOA)

Trigonometry provides relationships between the angles and sides of a right triangle. These ratios are crucial for solving triangles when angles are involved:

  • Sine (sin): Opposite / Hypotenuse (sin(A) = a/c, sin(B) = b/c)
  • Cosine (cos): Adjacent / Hypotenuse (cos(A) = b/c, cos(B) = a/c)
  • Tangent (tan): Opposite / Adjacent (tan(A) = a/b, tan(B) = b/a)

How to Use the Calculator

Our calculator is designed to be intuitive. You need to input at least two values, with at least one of them being a side length. The calculator will then determine all other unknown properties of the triangle.

  1. Identify Known Values: Look at your right angle triangle and identify which sides (a, b, or c) or acute angles (A or B) you know.
  2. Enter Values: Input your known values into the corresponding fields in the calculator. Leave the fields for unknown values blank.
  3. Click "Calculate Triangle": The calculator will process your inputs and display the calculated values for the remaining sides, angles, area, and perimeter.
  4. Review Results: The results section will show all the properties of your right angle triangle, rounded to four decimal places for precision.

Examples of Use

Example 1: Given Two Sides (Legs)

Suppose you have a right triangle with side 'a' = 3 units and side 'b' = 4 units.

  • Enter '3' in "Side 'a'".
  • Enter '4' in "Side 'b'".
  • Click "Calculate Triangle".

Expected Output:

  • Side a: 3.0000
  • Side b: 4.0000
  • Hypotenuse c: 5.0000 (from 3² + 4² = 5²)
  • Angle A: 36.8699 degrees (from atan(3/4))
  • Angle B: 53.1301 degrees (from 90 – 36.8699)
  • Angle C: 90 degrees
  • Area: 6.0000 (0.5 * 3 * 4)
  • Perimeter: 12.0000 (3 + 4 + 5)

Example 2: Given One Side and the Hypotenuse

Consider a right triangle where side 'a' = 6 units and the hypotenuse 'c' = 10 units.

  • Enter '6' in "Side 'a'".
  • Enter '10' in "Hypotenuse 'c'".
  • Click "Calculate Triangle".

Expected Output:

  • Side a: 6.0000
  • Side b: 8.0000 (from sqrt(10² – 6²))
  • Hypotenuse c: 10.0000
  • Angle A: 36.8699 degrees (from asin(6/10))
  • Angle B: 53.1301 degrees
  • Angle C: 90 degrees
  • Area: 24.0000
  • Perimeter: 24.0000

Example 3: Given One Side and One Acute Angle

Let's say you have side 'b' = 7 units and Angle A = 45 degrees.

  • Enter '7' in "Side 'b'".
  • Enter '45' in "Angle A (degrees)".
  • Click "Calculate Triangle".

Expected Output:

  • Side a: 7.0000 (from b * tan(A))
  • Side b: 7.0000
  • Hypotenuse c: 9.8995 (from b / cos(A))
  • Angle A: 45.0000 degrees
  • Angle B: 45.0000 degrees (from 90 – 45)
  • Angle C: 90 degrees
  • Area: 24.5000
  • Perimeter: 23.8995

This calculator simplifies complex trigonometric calculations, making it an invaluable tool for students, engineers, carpenters, and anyone working with right angle triangles.

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