Angle B (given sides A & B)
Side B (given side A & angle B)
Side A (given side B & angle B)
Hypotenuse (given sides A & B)
Hypotenuse (given side A & angle B)
Hypotenuse (given side B & angle B)
Angle B (given side A & hypotenuse)
Angle B (given side B & hypotenuse)
Results
Side A: –
Side B: –
Hypotenuse: –
Angle B: – degrees
Understanding Right Triangle Trigonometry
Right triangle trigonometry is a fundamental branch of mathematics that deals with the relationships between the sides and angles of right-angled triangles. A right-angled triangle is a triangle where one of the angles is exactly 90 degrees.
Key Components:
Hypotenuse: The side opposite the right angle. It is always the longest side of the right triangle.
Adjacent Side: The side that is next to the angle in question, but is not the hypotenuse.
Opposite Side: The side that is across from the angle in question.
Angles: A right triangle has three angles, one of which is 90 degrees. The sum of the other two acute angles is always 90 degrees.
The Trigonometric Ratios (SOH CAH TOA):
The core of right triangle trigonometry lies in the three primary trigonometric ratios:
Sine (sin): The ratio of the length of the opposite side to the length of the hypotenuse. sin(θ) = Opposite / Hypotenuse
Cosine (cos): The ratio of the length of the adjacent side to the length of the hypotenuse. cos(θ) = Adjacent / Hypotenuse
Tangent (tan): The ratio of the length of the opposite side to the length of the adjacent side. tan(θ) = Opposite / Adjacent
These ratios are typically remembered using the mnemonic SOH CAH TOA.
Inverse Trigonometric Functions:
When you know the ratio of two sides and need to find an angle, you use the inverse trigonometric functions:
Arcsine (arcsin or sin-1): Used to find an angle when you know the sine ratio.
Arccosine (arccos or cos-1): Used to find an angle when you know the cosine ratio.
Arctangent (arctan or tan-1): Used to find an angle when you know the tangent ratio.
Calculating Sides and Angles:
This calculator helps you find unknown sides or angles of a right triangle using the trigonometric relationships. You need to provide at least two known values (sides or angles) to solve for the others.
Angle B: Using the tangent function, tan(B) = Opposite/Adjacent = 8/6 = 1.333. Therefore, Angle B = arctan(1.333) ≈ 53.13 degrees.
This calculator streamlines these calculations, allowing for quick determination of unknown elements in right triangles, which is crucial in fields like engineering, physics, navigation, surveying, and geometry.
function calculateTrig() {
var sideA = parseFloat(document.getElementById("sideA").value);
var sideB = parseFloat(document.getElementById("sideB").value);
var hypotenuse = parseFloat(document.getElementById("hypotenuse").value);
var angleRad = parseFloat(document.getElementById("angle").value) * (Math.PI / 180); // Convert degrees to radians
var operation = document.getElementById("operation").value;
var resultSideA = document.getElementById("resultSideA");
var resultSideB = document.getElementById("resultSideB");
var resultHypotenuse = document.getElementById("resultHypotenuse");
var resultAngleB = document.getElementById("resultAngleB");
var errorMessage = document.getElementById("errorMessage");
// Clear previous results and error messages
resultSideA.textContent = "-";
resultSideB.textContent = "-";
resultHypotenuse.textContent = "-";
resultAngleB.textContent = "-";
errorMessage.textContent = "";
var angleDeg;
// — Calculations —
// Angle B from sides A and B (using arctan)
if (operation === "angleB") {
if (!isNaN(sideA) && !isNaN(sideB) && sideA > 0 && sideB > 0) {
angleDeg = Math.atan(sideB / sideA) * (180 / Math.PI);
resultAngleB.textContent = angleDeg.toFixed(2);
// Calculate hypotenuse using Pythagorean theorem
var calculatedHypotenuse = Math.sqrt(Math.pow(sideA, 2) + Math.pow(sideB, 2));
resultHypotenuse.textContent = calculatedHypotenuse.toFixed(2);
// Display provided sides
resultSideA.textContent = sideA.toFixed(2);
resultSideB.textContent = sideB.toFixed(2);
} else {
errorMessage.textContent = "Please provide valid positive values for Side A and Side B to calculate Angle B.";
}
}
// Side B from side A and angle B
else if (operation === "sideB") {
if (!isNaN(sideA) && !isNaN(angleRad) && sideA > 0 && angleRad > 0 && angleRad