Calculate Triangle Sides

Right-Angled Triangle Side & Angle Calculator

function calculateTriangle() { var sideA_input = parseFloat(document.getElementById('sideA').value); var sideB_input = parseFloat(document.getElementById('sideB').value); var hypotenuse_input = parseFloat(document.getElementById('hypotenuse').value); var angleA_input = parseFloat(document.getElementById('angleA').value); // degrees var angleB_input = parseFloat(document.getElementById('angleB').value); // degrees var a = isNaN(sideA_input) || sideA_input <= 0 ? NaN : sideA_input; var b = isNaN(sideB_input) || sideB_input <= 0 ? NaN : sideB_input; var c = isNaN(hypotenuse_input) || hypotenuse_input <= 0 ? NaN : hypotenuse_input; var alphaRad = isNaN(angleA_input) || angleA_input = 90 ? NaN : angleA_input * Math.PI / 180; var betaRad = isNaN(angleB_input) || angleB_input = 90 ? NaN : angleB_input * Math.PI / 180; var knownCount = 0; if (!isNaN(a)) knownCount++; if (!isNaN(b)) knownCount++; if (!isNaN(c)) knownCount++; if (!isNaN(alphaRad)) knownCount++; if (!isNaN(betaRad)) knownCount++; var resultDiv = document.getElementById('triangleResult'); resultDiv.innerHTML = "; // Clear previous results if (knownCount < 2) { resultDiv.innerHTML = 'Please enter at least two valid positive values (sides or angles less than 90 degrees) for a right-angled triangle.'; return; } var changed = true; var iterationCount = 0; var maxIterations = 10; // Prevent infinite loops in case of complex dependencies while (changed && iterationCount = c) { resultDiv.innerHTML = 'Side A must be less than the Hypotenuse.'; return; } alphaRad = Math.asin(a / c); changed = true; } if (!isNaN(a) && !isNaN(c) && isNaN(betaRad)) { if (a >= c) { resultDiv.innerHTML = 'Side A must be less than the Hypotenuse.'; return; } betaRad = Math.acos(a / c); changed = true; } if (!isNaN(b) && !isNaN(c) && isNaN(betaRad)) { if (b >= c) { resultDiv.innerHTML = 'Side B must be less than the Hypotenuse.'; return; } betaRad = Math.asin(b / c); changed = true; } if (!isNaN(b) && !isNaN(c) && isNaN(alphaRad)) { if (b >= c) { resultDiv.innerHTML = 'Side B must be less than the Hypotenuse.'; return; } alphaRad = Math.acos(b / c); changed = true; } // Try to find missing side if two sides are known (Pythagorean) if (!isNaN(a) && !isNaN(b) && isNaN(c)) { c = Math.sqrt(a * a + b * b); changed = true; } if (!isNaN(a) && !isNaN(c) && isNaN(b)) { var b_squared = c * c – a * a; if (b_squared <= 0) { resultDiv.innerHTML = 'Side A cannot be greater than or equal to the Hypotenuse.'; return; } b = Math.sqrt(b_squared); changed = true; } if (!isNaN(b) && !isNaN(c) && isNaN(a)) { var a_squared = c * c – b * b; if (a_squared <= 0) { resultDiv.innerHTML = 'Side B cannot be greater than or equal to the Hypotenuse.'; return; } a = Math.sqrt(a_squared); changed = true; } // Try to find missing angle if one angle is known if (!isNaN(alphaRad) && isNaN(betaRad)) { betaRad = Math.PI / 2 – alphaRad; changed = true; } if (!isNaN(betaRad) && isNaN(alphaRad)) { alphaRad = Math.PI / 2 – betaRad; changed = true; } // Try to find missing sides if one side and one angle are known if (!isNaN(a) && !isNaN(alphaRad)) { if (isNaN(b)) { b = a / Math.tan(alphaRad); changed = true; } if (isNaN(c)) { c = a / Math.sin(alphaRad); changed = true; } } if (!isNaN(a) && !isNaN(betaRad)) { if (isNaN(b)) { b = a * Math.tan(betaRad); changed = true; } if (isNaN(c)) { c = a / Math.cos(betaRad); changed = true; } } if (!isNaN(b) && !isNaN(alphaRad)) { if (isNaN(a)) { a = b * Math.tan(alphaRad); changed = true; } if (isNaN(c)) { c = b / Math.cos(alphaRad); changed = true; } } if (!isNaN(b) && !isNaN(betaRad)) { if (isNaN(a)) { a = b / Math.tan(betaRad); changed = true; } if (isNaN(c)) { c = b / Math.sin(betaRad); changed = true; } } if (!isNaN(c) && !isNaN(alphaRad)) { if (isNaN(a)) { a = c * Math.sin(alphaRad); changed = true; } if (isNaN(b)) { b = c * Math.cos(alphaRad); changed = true; } } if (!isNaN(c) && !isNaN(betaRad)) { if (isNaN(a)) { a = c * Math.cos(betaRad); changed = true; } if (isNaN(b)) { b = c * Math.sin(betaRad); changed = true; } } } // Final consistency checks and display var outputHTML = '

Calculated Triangle Properties:

'; var allKnown = !isNaN(a) && !isNaN(b) && !isNaN(c) && !isNaN(alphaRad) && !isNaN(betaRad); if (!allKnown) { resultDiv.innerHTML = 'Could not calculate all missing values with the given inputs. Please ensure at least two independent values are provided that define a unique right-angled triangle.'; return; } // Convert angles back to degrees for display var alphaDeg = alphaRad * 180 / Math.PI; var betaDeg = betaRad * 180 / Math.PI; // Rounding for display a = parseFloat(a.toFixed(4)); b = parseFloat(b.toFixed(4)); c = parseFloat(c.toFixed(4)); alphaDeg = parseFloat(alphaDeg.toFixed(4)); betaDeg = parseFloat(betaDeg.toFixed(4)); outputHTML += 'Side A (Opposite Angle A): ' + a + "; outputHTML += 'Side B (Opposite Angle B): ' + b + "; outputHTML += 'Hypotenuse (Side C): ' + c + "; outputHTML += 'Angle A: ' + alphaDeg + ' degrees'; outputHTML += 'Angle B: ' + betaDeg + ' degrees'; outputHTML += 'Note: This calculator assumes a right-angled triangle (one angle is 90 degrees).'; resultDiv.innerHTML = outputHTML; } function clearForm() { document.getElementById('sideA').value = "; document.getElementById('sideB').value = "; document.getElementById('hypotenuse').value = "; document.getElementById('angleA').value = "; document.getElementById('angleB').value = "; document.getElementById('triangleResult').innerHTML = "; }

Understanding Right-Angled Triangles and Their Calculations

A right-angled triangle is a fundamental shape in geometry, characterized by one angle measuring exactly 90 degrees. This unique property allows for straightforward calculations of its sides and other angles using specific mathematical principles: the Pythagorean theorem and trigonometric ratios.

Key Components of a Right-Angled Triangle

• Hypotenuse (Side C): This is the longest side of the right-angled triangle, always opposite the 90-degree angle.
• Side A (Opposite Angle A): The side opposite to angle A.
• Side B (Opposite Angle B): The side opposite to angle B.
• Angles A and B: These are the two acute angles (less than 90 degrees) in the triangle. The sum of Angle A and Angle B always equals 90 degrees.

The Pythagorean Theorem

The Pythagorean theorem is a cornerstone for calculating the sides of a right-angled triangle when two sides are known. It states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

a² + b² = c²

This theorem is invaluable when you know any two sides and need to find the third.

Trigonometric Ratios (SOH CAH TOA)

When you know one side and one acute angle (or two sides and need to find an angle), trigonometric ratios come into play. These ratios relate the angles of a right-angled triangle to the lengths of its sides:

• Sine (SOH): Sine(Angle) = Opposite / Hypotenuse
• Cosine (CAH): Cosine(Angle) = Adjacent / Hypotenuse
• Tangent (TOA): Tangent(Angle) = Opposite / Adjacent

To find an angle when two sides are known, you use the inverse trigonometric functions (arcsin, arccos, arctan).

How to Use the Calculator

Our Right-Angled Triangle Side & Angle Calculator simplifies these complex calculations. To use it:

1. Enter at least two values: You must provide at least two known values for the triangle. This can be any combination of two sides, one side and one angle, or even two angles (though two angles alone won't determine side lengths without at least one side).
2. Input positive numbers: Ensure all entered values are positive. Angles must be less than 90 degrees.
3. Click "Calculate": The calculator will automatically determine all the missing sides and angles of the right-angled triangle.
4. Review Results: The calculated values for Side A, Side B, Hypotenuse, Angle A, and Angle B will be displayed.
5. "Clear" button: Use this to reset all input fields and results for a new calculation.

Examples of Triangle Calculations

Example 1: Finding Hypotenuse and Angles (Given Two Sides)

Imagine you have a right-angled triangle where Side A = 3 units and Side B = 4 units.

• Input: Side A = 3, Side B = 4
• Calculation:
  • Hypotenuse (c): Using Pythagorean theorem, c = √(3² + 4²) = √(9 + 16) = √25 = 5 units.
  • Angle A: tan(A) = Opposite/Adjacent = 3/4 → A = arctan(0.75) ≈ 36.87 degrees.
  • Angle B: tan(B) = Opposite/Adjacent = 4/3 → B = arctan(1.333) ≈ 53.13 degrees. (Also, B = 90 – A)
• Result: Side C = 5, Angle A ≈ 36.87°, Angle B ≈ 53.13°

Example 2: Finding Sides and an Angle (Given Hypotenuse and One Angle)

Suppose the Hypotenuse = 10 units and Angle A = 30 degrees.

• Input: Hypotenuse = 10, Angle A = 30
• Calculation:
  • Angle B: B = 90 – 30 = 60 degrees.
  • Side A: sin(A) = Opposite/Hypotenuse → sin(30°) = A/10 → A = 10 * sin(30°) = 10 * 0.5 = 5 units.
  • Side B: cos(A) = Adjacent/Hypotenuse → cos(30°) = B/10 → B = 10 * cos(30°) ≈ 10 * 0.866 = 8.66 units.
• Result: Side A = 5, Side B ≈ 8.66, Angle B = 60°

Example 3: Finding Hypotenuse, a Side, and an Angle (Given One Side and One Angle)

Let Side A = 5 units and Angle B = 60 degrees.

• Input: Side A = 5, Angle B = 60
• Calculation:
  • Angle A: A = 90 – 60 = 30 degrees.
  • Side B: tan(B) = Opposite/Adjacent = B/A → tan(60°) = B/5 → B = 5 * tan(60°) ≈ 5 * 1.732 = 8.66 units.
  • Hypotenuse (c): sin(A) = Opposite/Hypotenuse → sin(30°) = 5/c → c = 5 / sin(30°) = 5 / 0.5 = 10 units.
• Result: Side B ≈ 8.66, Side C = 10, Angle A = 30°

This calculator is a handy tool for students, engineers, architects, and anyone needing quick and accurate right-angled triangle calculations.