Trig Calculator Triangle

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Trigonometry Triangle Calculator .trig-calculator-container { font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif; max-width: 800px; margin: 20px auto; padding: 25px; border: 1px solid #e0e0e0; border-radius: 12px; background-color: #f9f9f9; color: #333; box-shadow: 0 4px 6px rgba(0,0,0,0.05); } .trig-calculator-container h2 { text-align: center; color: #2c3e50; margin-bottom: 25px; } .trig-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 20px; margin-bottom: 20px; } .trig-input-group { display: flex; flex-direction: column; } .trig-input-group label { font-weight: 600; margin-bottom: 8px; color: #4a5568; } .trig-input-group input { padding: 10px; border: 1px solid #cbd5e0; border-radius: 6px; font-size: 16px; } .trig-btn-container { display: flex; gap: 10px; justify-content: center; margin-top: 10px; } .trig-calc-btn { background-color: #3182ce; color: white; border: none; padding: 12px 24px; border-radius: 6px; cursor: pointer; font-size: 16px; font-weight: bold; transition: background-color 0.2s; } .trig-calc-btn:hover { background-color: #2b6cb0; } .trig-reset-btn { background-color: #e2e8f0; color: #4a5568; border: none; padding: 12px 24px; border-radius: 6px; cursor: pointer; font-size: 16px; } .trig-results { margin-top: 25px; padding: 20px; background-color: #fff; border-radius: 8px; border-left: 5px solid #3182ce; display: none; } .trig-results h3 { margin-top: 0; font-size: 1.2rem; color: #2d3748; } .trig-results-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 10px; } .res-item { padding: 8px; border-bottom: 1px solid #edf2f7; } .res-label { font-weight: bold; color: #718096; } .article-content { margin-top: 40px; line-height: 1.6; color: #4a5568; } .article-content h3 { color: #2d3748; border-bottom: 2px solid #edf2f7; padding-bottom: 8px; margin-top: 30px; } .article-content ul { padding-left: 20px; } @media (max-width: 600px) { .trig-grid { grid-template-columns: 1fr; } }

Right-Angled Triangle Solver

Enter any two values (at least one must be a side) to solve the triangle.

Calculation Results

Side a: –
Side b: –
Side c (Hyp): –
Angle A: –°
Angle B: –°
Angle C: 90°
Area: –
Perimeter: –

Understanding Right-Angled Trigonometry

A right-angled triangle is a polygon with three sides and three angles, where one of the angles is exactly 90 degrees. Trigonometry is the branch of mathematics that studies the relationships between the lengths of these sides and the angles between them.

The Fundamental Formulas

To solve for unknown parts of a right triangle, we primarily use the Pythagorean Theorem and the three basic trigonometric ratios:

  • Pythagorean Theorem: a² + b² = c² (where c is the hypotenuse).
  • Sine (sin): Opposite / Hypotenuse (sin A = a / c).
  • Cosine (cos): Adjacent / Hypotenuse (cos A = b / c).
  • Tangent (tan): Opposite / Adjacent (tan A = a / b).

Common Triangle Examples

The "3-4-5" triangle is the most famous example of a right triangle. If Side a = 3 and Side b = 4, the hypotenuse Side c will always be 5. The angles in such a triangle are approximately 36.87° and 53.13°.

How to Use This Calculator

This tool is designed to save time on complex geometry homework or engineering tasks. Simply input any two known dimensions. Note that you must provide at least one side length; providing only two angles is not enough to determine the size of the triangle, as infinite triangles can share the same angles (similar triangles).

Why Trigonometry Matters

Beyond the classroom, trigonometry is used in architecture to calculate roof slopes, in navigation to determine distances across oceans, and in physics to understand wave patterns and projectile motion.

function calculateTriangle() { var a = parseFloat(document.getElementById('sideA').value); var b = parseFloat(document.getElementById('sideB').value); var c = parseFloat(document.getElementById('sideC').value); var degA = parseFloat(document.getElementById('angleA').value); var degB = parseFloat(document.getElementById('angleB').value); var count = 0; if (!isNaN(a)) count++; if (!isNaN(b)) count++; if (!isNaN(c)) count++; if (!isNaN(degA)) count++; if (!isNaN(degB)) count++; if (count = c) { alert("Hypotenuse must be longer than side a."); return; } b = Math.sqrt(c * c – a * a); radA = Math.asin(a / c); radB = Math.acos(a / c); } else if (!isNaN(b) && !isNaN(c)) { if (b >= c) { alert("Hypotenuse must be longer than side b."); return; } a = Math.sqrt(c * c – b * b); radA = Math.acos(b / c); radB = Math.asin(b / c); } // Case 2: Side and Angle else if (!isNaN(a) && !isNaN(degA)) { radA = degA * (Math.PI / 180); c = a / Math.sin(radA); b = a / Math.tan(radA); radB = (Math.PI / 2) – radA; } else if (!isNaN(a) && !isNaN(degB)) { radB = degB * (Math.PI / 180); c = a / Math.cos(radB); b = a * Math.tan(radB); radA = (Math.PI / 2) – radB; } else if (!isNaN(b) && !isNaN(degA)) { radA = degA * (Math.PI / 180); c = b / Math.cos(radA); a = b * Math.tan(radA); radB = (Math.PI / 2) – radA; } else if (!isNaN(b) && !isNaN(degB)) { radB = degB * (Math.PI / 180); c = b / Math.sin(radB); a = b / Math.tan(radB); radA = (Math.PI / 2) – radB; } else if (!isNaN(c) && !isNaN(degA)) { radA = degA * (Math.PI / 180); a = c * Math.sin(radA); b = c * Math.cos(radA); radB = (Math.PI / 2) – radA; } else if (!isNaN(c) && !isNaN(degB)) { radB = degB * (Math.PI / 180); a = c * Math.cos(radB); b = c * Math.sin(radB); radA = (Math.PI / 2) – radB; } degA = radA * (180 / Math.PI); degB = radB * (180 / Math.PI); var area = 0.5 * a * b; var perimeter = a + b + c; // Display document.getElementById('resA').innerText = a.toFixed(4); document.getElementById('resB').innerText = b.toFixed(4); document.getElementById('resC').innerText = c.toFixed(4); document.getElementById('resAngA').innerText = degA.toFixed(4); document.getElementById('resAngB').innerText = degB.toFixed(4); document.getElementById('resArea').innerText = area.toFixed(4); document.getElementById('resPeri').innerText = perimeter.toFixed(4); document.getElementById('trigResults').style.display = 'block'; } function resetTrig() { document.getElementById('sideA').value = "; document.getElementById('sideB').value = "; document.getElementById('sideC').value = "; document.getElementById('angleA').value = "; document.getElementById('angleB').value = "; document.getElementById('trigResults').style.display = 'none'; }

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