Enter at least two known values to calculate the rest.
Understanding Right Triangles and Their Calculations
A right triangle is a fundamental geometric shape characterized by having one angle that measures exactly 90 degrees (a right angle). The sides adjacent to the right angle are called "legs" (often denoted as 'a' and 'b'), and the side opposite the right angle is called the "hypotenuse" (denoted as 'c'). This calculator helps you determine unknown sides and angles of a right triangle when you provide at least two known values.
The Pythagorean Theorem
The most famous property of right triangles is the Pythagorean Theorem, which relates the lengths of the three sides. 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 allows us to find the length of any side if the other two are known. For example, if you know sides 'a' and 'b', you can find 'c' by calculating c = √(a² + b²). If you know 'c' and 'a', you can find 'b' using b = √(c² - a²).
Trigonometric Functions (SOH CAH TOA)
Beyond the Pythagorean theorem, trigonometric functions are essential for relating angles and side lengths. The primary trigonometric ratios in a right triangle are:
Sine (sin):sin(angle) = Opposite / Hypotenuse (SOH)
Using these, along with their inverse functions (arcsin, arccos, arctan), we can determine unknown angles if we know two sides, or find unknown sides if we know one side and one acute angle.
Angles in a Right Triangle
A crucial property is that the sum of all angles in any triangle is 180 degrees. In a right triangle, since one angle is 90 degrees, the sum of the other two acute angles must be 90 degrees:
Angle A + Angle B = 90°
Use Cases
Right triangle calculations are fundamental in various fields:
Construction and Architecture: Ensuring square corners, calculating roof pitches, and determining diagonal lengths for bracing.
Navigation: Calculating distances and bearings.
Engineering: Analyzing forces, designing structures, and solving problems in physics.
Surveying: Measuring distances and heights that are difficult to access directly.
Computer Graphics: Positioning objects and calculating transformations in 2D and 3D space.
This calculator simplifies these calculations, providing quick and accurate results for anyone working with right triangles.
function calculateRightTriangle() {
var sideAInput = document.getElementById("sideA");
var sideBInput = document.getElementById("sideB");
var hypotenuseInput = document.getElementById("hypotenuse");
var angleAInput = document.getElementById("angleA");
var angleBInput = document.getElementById("angleB");
var resultDiv = document.getElementById("result");
var sideA = parseFloat(sideAInput.value);
var sideB = parseFloat(sideBInput.value);
var hypotenuse = parseFloat(hypotenuseInput.value);
var angleA = parseFloat(angleAInput.value);
var angleB = parseFloat(angleBInput.value);
var results = {};
var knownValuesCount = 0;
// Check which values are provided and valid
if (!isNaN(sideA) && sideA > 0) knownValuesCount++;
if (!isNaN(sideB) && sideB > 0) knownValuesCount++;
if (!isNaN(hypotenuse) && hypotenuse > 0) knownValuesCount++;
if (!isNaN(angleA) && angleA > 0 && angleA 0 && angleB 0 && sideB > 0) {
hypotenuse = Math.sqrt(sideA * sideA + sideB * sideB);
angleA = (Math.atan(sideA / sideB) * 180) / Math.PI;
angleB = 90 – angleA;
results = { sideA: sideA, sideB: sideB, hypotenuse: hypotenuse, angleA: angleA, angleB: angleB };
} else if (!isNaN(sideA) && !isNaN(hypotenuse) && sideA > 0 && hypotenuse > 0 && hypotenuse > sideA) {
sideB = Math.sqrt(hypotenuse * hypotenuse – sideA * sideA);
angleA = (Math.asin(sideA / hypotenuse) * 180) / Math.PI;
angleB = 90 – angleA;
results = { sideA: sideA, sideB: sideB, hypotenuse: hypotenuse, angleA: angleA, angleB: angleB };
} else if (!isNaN(sideB) && !isNaN(hypotenuse) && sideB > 0 && hypotenuse > 0 && hypotenuse > sideB) {
sideA = Math.sqrt(hypotenuse * hypotenuse – sideB * sideB);
angleB = (Math.asin(sideB / hypotenuse) * 180) / Math.PI;
angleA = 90 – angleB;
results = { sideA: sideA, sideB: sideB, hypotenuse: hypotenuse, angleA: angleA, angleB: angleB };
}
// If one side and one angle are known
else if (!isNaN(sideA) && !isNaN(angleA) && sideA > 0 && angleA > 0 && angleA 0 && angleB > 0 && angleB 0 && angleA > 0 && angleA 0 && angleB > 0 && angleB 0 && angleA > 0 && angleA 0 && angleB > 0 && angleB 0;
if (calculatedValues) {
sideAInput.value = isNaN(results.sideA) ? "" : results.sideA.toFixed(4);
sideBInput.value = isNaN(results.sideB) ? "" : results.sideB.toFixed(4);
hypotenuseInput.value = isNaN(results.hypotenuse) ? "" : results.hypotenuse.toFixed(4);
angleAInput.value = isNaN(results.angleA) ? "" : results.angleA.toFixed(4);
angleBInput.value = isNaN(results.angleB) ? "" : results.angleB.toFixed(4);
resultDiv.innerHTML = "Side A: " + results.sideA.toFixed(4) + " | Side B: " + results.sideB.toFixed(4) +
" | Hypotenuse: " + results.hypotenuse.toFixed(4) + " | Angle A: " + results.angleA.toFixed(4) + "° | Angle B: " + results.angleB.toFixed(4) + "°";
} else {
if (knownValuesCount < 2) {
resultDiv.innerHTML = "Please enter at least two known values to calculate the rest.";
} else {
resultDiv.innerHTML = "Insufficient or invalid information provided. Please ensure you have at least two valid measurements (sides must be positive, angles between 0 and 90 degrees).";
}
}
}