Right Triangle Angle Calculator
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Right Triangle Angle Calculator
Enter two known values of a right triangle to calculate the unknown angles.
Side A (Adjacent to Angle B):
Side B (Opposite to Angle A):
Hypotenuse (C):
Known Value 1:
Type of Known Value 1:
Side A (Adjacent to Angle B)
Side B (Opposite to Angle A)
Hypotenuse (C)
Angle A (degrees)
Angle B (degrees)
Known Value 2:
Type of Known Value 2:
Side A (Adjacent to Angle B)
Side B (Opposite to Angle A)
Hypotenuse (C)
Angle A (degrees)
Angle B (degrees)
Calculate Angles
Understanding Right Triangle Angles and Calculations
A right triangle is a fundamental geometric shape defined by having one angle exactly equal to 90 degrees. The sides opposite the right angle is called the hypotenuse, and the other two sides are called legs. Calculating the angles of a right triangle is crucial in various fields, including trigonometry, physics, engineering, architecture, and navigation.
In a right triangle, let's denote the angles as follows:
Angle C = 90 degrees (the right angle)
Angle A (one of the acute angles)
Angle B (the other acute angle)
And the sides opposite these angles:
Side C (Hypotenuse)
Side A (Opposite Angle A, Adjacent to Angle B)
Side B (Opposite Angle B, Adjacent to Angle A)
The sum of angles in any triangle is always 180 degrees. Therefore, in a right triangle:
Angle A + Angle B + Angle C = 180 degrees
Since Angle C is 90 degrees, this simplifies to:
Angle A + Angle B = 90 degrees
This means that the two acute angles in a right triangle are complementary; they add up to 90 degrees.
We can use trigonometric functions (sine, cosine, tangent) to find unknown angles if we know the lengths of the sides.
Sine (sin): sin(angle) = Opposite / HypotenuseCosine (cos): cos(angle) = Adjacent / HypotenuseTangent (tan): tan(angle) = Opposite / Adjacent
To find the angle, we use the inverse trigonometric functions (arcsine, arccosine, arctangent):
Angle A = arcsin(Side B / Hypotenuse)
Angle A = arccos(Side A / Hypotenuse)
Angle A = arctan(Side B / Side A)
Similarly for Angle B:
Angle B = arcsin(Side A / Hypotenuse)
Angle B = arccos(Side B / Hypotenuse)
Angle B = arctan(Side A / Side B)
This calculator allows you to input two known values (sides or angles) of a right triangle. Based on these inputs, it calculates the remaining unknown values, including the other two angles and any unknown sides.
Example Usage:
If you know Side A = 3 units and Side B = 4 units:
You would input '3' for 'Known Value 1' and select 'Side A (Adjacent to Angle B)' for 'Type of Known Value 1'.
You would input '4' for 'Known Value 2' and select 'Side B (Opposite to Angle A)' for 'Type of Known Value 2'.
The calculator would then compute:
Hypotenuse (C) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5 units.
Angle A = arctan(Side B / Side A) = arctan(4 / 3) ≈ 53.13 degrees.
Angle B = 90 – Angle A ≈ 90 – 53.13 = 36.87 degrees.
If you know Side A = 5 units and Angle A = 30 degrees:
You would input '5' for 'Known Value 1' and select 'Side A (Adjacent to Angle B)' for 'Type of Known Value 1'.
You would input '30' for 'Known Value 2' and select 'Angle A (degrees)' for 'Type of Known Value 2'.
The calculator would then compute:
tan(30°) = Side B / Side A => Side B = Side A * tan(30°) = 5 * (1/√3) ≈ 2.89 units.
Hypotenuse (C) = Side A / cos(30°) = 5 / (√3/2) ≈ 5.77 units.
Angle B = 90° – Angle A = 90° – 30° = 60 degrees.
function calculateAngles() {
var sideAInput = document.getElementById("sideA");
var sideBInput = document.getElementById("sideB");
var hypotenuseInput = document.getElementById("hypotenuse");
var knownValue1Input = document.getElementById("knownValue1");
var valueType1 = document.getElementById("valueType1").value;
var knownValue2Input = document.getElementById("knownValue2");
var valueType2 = document.getElementById("valueType2").value;
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = "; // Clear previous results
var sideA = parseFloat(sideAInput.value);
var sideB = parseFloat(sideBInput.value);
var hypotenuse = parseFloat(hypotenuseInput.value);
var knownValue1 = parseFloat(knownValue1Input.value);
var knownValue2 = parseFloat(knownValue2Input.value);
var calculatedSideA = null;
var calculatedSideB = null;
var calculatedHypotenuse = null;
var calculatedAngleA = null; // in degrees
var calculatedAngleB = null; // in degrees
var values = {};
values[valueType1] = knownValue1;
values[valueType2] = knownValue2;
// — Input Validation —
if (isNaN(knownValue1) || isNaN(knownValue2) || valueType1 === valueType2) {
resultDiv.innerHTML = "Please enter two distinct valid known values.";
return;
}
// If sides are pre-filled and valid, use them
if (!isNaN(sideA) && sideA > 0) values['sideA'] = sideA;
if (!isNaN(sideB) && sideB > 0) values['sideB'] = sideB;
if (!isNaN(hypotenuse) && hypotenuse > 0) values['hypotenuse'] = hypotenuse;
// — Calculation Logic —
// Case 1: Two sides known
if (values['sideA'] !== undefined && values['sideB'] !== undefined) {
calculatedSideA = values['sideA'];
calculatedSideB = values['sideB'];
calculatedHypotenuse = Math.sqrt(calculatedSideA * calculatedSideA + calculatedSideB * calculatedSideB);
} else if (values['sideA'] !== undefined && values['hypotenuse'] !== undefined) {
calculatedSideA = values['sideA'];
calculatedHypotenuse = values['hypotenuse'];
if (calculatedHypotenuse > calculatedSideA) {
calculatedSideB = Math.sqrt(calculatedHypotenuse * calculatedHypotenuse – calculatedSideA * calculatedSideA);
} else {
resultDiv.innerHTML = "Hypotenuse cannot be smaller than Side A.";
return;
}
} else if (values['sideB'] !== undefined && values['hypotenuse'] !== undefined) {
calculatedSideB = values['sideB'];
calculatedHypotenuse = values['hypotenuse'];
if (calculatedHypotenuse > calculatedSideB) {
calculatedSideA = Math.sqrt(calculatedHypotenuse * calculatedHypotenuse – calculatedSideB * calculatedSideB);
} else {
resultDiv.innerHTML = "Hypotenuse cannot be smaller than Side B.";
return;
}
}
// Case 2: One side and one angle known
if (calculatedSideA === null && calculatedSideB === null && calculatedHypotenuse === null) {
if (values['sideA'] !== undefined && values['angleA'] !== undefined) {
calculatedSideA = values['sideA'];
var angleA_rad = values['angleA'] * Math.PI / 180;
calculatedAngleA = values['angleA'];
if (Math.cos(angleA_rad) !== 0) {
calculatedHypotenuse = calculatedSideA / Math.cos(angleA_rad);
calculatedSideB = calculatedSideA * Math.tan(angleA_rad);
} else {
resultDiv.innerHTML = "Invalid angle for calculating side B or hypotenuse with Side A.";
return;
}
} else if (values['sideA'] !== undefined && values['angleB'] !== undefined) {
calculatedSideA = values['sideA'];
calculatedAngleB = values['angleB'];
var angleB_rad = values['angleB'] * Math.PI / 180;
if (Math.tan(angleB_rad) !== 0) {
calculatedSideB = calculatedSideA / Math.tan(angleB_rad);
calculatedHypotenuse = calculatedSideA / Math.sin(angleB_rad);
} else {
resultDiv.innerHTML = "Invalid angle for calculating side B or hypotenuse with Side A.";
return;
}
} else if (values['sideB'] !== undefined && values['angleA'] !== undefined) {
calculatedSideB = values['sideB'];
calculatedAngleA = values['angleA'];
var angleA_rad = values['angleA'] * Math.PI / 180;
if (Math.tan(angleA_rad) !== 0) {
calculatedSideA = calculatedSideB / Math.tan(angleA_rad);
calculatedHypotenuse = calculatedSideB / Math.sin(angleA_rad);
} else {
resultDiv.innerHTML = "Invalid angle for calculating side A or hypotenuse with Side B.";
return;
}
} else if (values['sideB'] !== undefined && values['angleB'] !== undefined) {
calculatedSideB = values['sideB'];
var angleB_rad = values['angleB'] * Math.PI / 180;
calculatedAngleB = values['angleB'];
if (Math.cos(angleB_rad) !== 0) {
calculatedHypotenuse = calculatedSideB / Math.cos(angleB_rad);
calculatedSideA = calculatedSideB * Math.tan(angleB_rad);
} else {
resultDiv.innerHTML = "Invalid angle for calculating side A or hypotenuse with Side B.";
return;
}
} else if (values['hypotenuse'] !== undefined && values['angleA'] !== undefined) {
calculatedHypotenuse = values['hypotenuse'];
calculatedAngleA = values['angleA'];
var angleA_rad = values['angleA'] * Math.PI / 180;
calculatedSideB = calculatedHypotenuse * Math.sin(angleA_rad);
calculatedSideA = calculatedHypotenuse * Math.cos(angleA_rad);
} else if (values['hypotenuse'] !== undefined && values['angleB'] !== undefined) {
calculatedHypotenuse = values['hypotenuse'];
calculatedAngleB = values['angleB'];
var angleB_rad = values['angleB'] * Math.PI / 180;
calculatedSideA = calculatedHypotenuse * Math.sin(angleB_rad);
calculatedSideB = calculatedHypotenuse * Math.cos(angleB_rad);
}
}
// Calculate remaining angles if one is known or derived
if (calculatedAngleA === null && calculatedAngleB !== null) {
calculatedAngleA = 90 – calculatedAngleB;
} else if (calculatedAngleB === null && calculatedAngleA !== null) {
calculatedAngleB = 90 – calculatedAngleA;
}
// If no angles were directly given but sides are known, calculate them
if (calculatedAngleA === null && calculatedSideA !== null && calculatedSideB !== null) {
if (calculatedSideA > 0 && calculatedSideB > 0) {
calculatedAngleA = Math.atan(calculatedSideB / calculatedSideA) * 180 / Math.PI;
}
}
if (calculatedAngleB === null && calculatedSideA !== null && calculatedSideB !== null) {
if (calculatedSideA > 0 && calculatedSideB > 0) {
calculatedAngleB = Math.atan(calculatedSideA / calculatedSideB) * 180 / Math.PI;
}
}
// Ensure angles don't exceed 90 if they are acute angles in a right triangle
if (calculatedAngleA !== null && calculatedAngleA > 90) calculatedAngleA = 180 – calculatedAngleA;
if (calculatedAngleB !== null && calculatedAngleB > 90) calculatedAngleB = 180 – calculatedAngleB;
// — Display Results —
var displayResults = [];
if (!isNaN(calculatedSideA) && calculatedSideA !== null) displayResults.push("Side A (Adjacent to Angle B): " + calculatedSideA.toFixed(2));
if (!isNaN(calculatedSideB) && calculatedSideB !== null) displayResults.push("Side B (Opposite to Angle A): " + calculatedSideB.toFixed(2));
if (!isNaN(calculatedHypotenuse) && calculatedHypotenuse !== null) displayResults.push("Hypotenuse (C): " + calculatedHypotenuse.toFixed(2));
if (!isNaN(calculatedAngleA) && calculatedAngleA !== null) displayResults.push("Angle A: " + calculatedAngleA.toFixed(2) + "°");
if (!isNaN(calculatedAngleB) && calculatedAngleB !== null) displayResults.push("Angle B: " + calculatedAngleB.toFixed(2) + "°");
if (displayResults.length > 0) {
for (var i = 0; i < displayResults.length; i++) {
resultDiv.innerHTML += "
" + displayResults[i] + "
";
}
} else {
resultDiv.innerHTML = "Could not calculate. Please check your inputs.";
}
}