.calculator-container {
font-family: 'Arial', sans-serif;
max-width: 600px;
margin: 20px auto;
padding: 20px;
border: 1px solid #ddd;
border-radius: 8px;
box-shadow: 0 2px 4px rgba(0, 0, 0, 0.1);
}
.calculator-title {
text-align: center;
color: #333;
margin-bottom: 20px;
}
.calculator-inputs {
display: grid;
grid-template-columns: repeat(2, 1fr);
gap: 15px;
margin-bottom: 20px;
}
.input-group {
display: flex;
flex-direction: column;
}
.input-group label {
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.input-group input {
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1rem;
box-sizing: border-box; /* Ensures padding doesn't affect width */
}
.calculator-button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: #007bff;
color: white;
border: none;
border-radius: 4px;
font-size: 1.1rem;
cursor: pointer;
transition: background-color 0.3s ease;
}
.calculator-button:hover {
background-color: #0056b3;
}
.calculator-result {
margin-top: 20px;
padding: 15px;
background-color: #e9ecef;
border-radius: 4px;
text-align: center;
font-size: 1.1rem;
color: #333;
}
function calculateTrig() {
var sideA = parseFloat(document.getElementById("sideA").value);
var sideB = parseFloat(document.getElementById("sideB").value);
var hypotenuse = parseFloat(document.getElementById("hypotenuse").value);
var angleTheta = parseFloat(document.getElementById("angleTheta").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
// Determine which values are provided to calculate the rest
var calculated = false;
// Case 1: Two sides given (calculate hypotenuse and angles)
if (!isNaN(sideA) && !isNaN(sideB) && isNaN(hypotenuse) && isNaN(angleTheta)) {
var calculatedHypotenuse = Math.sqrt(sideA * sideA + sideB * sideB);
var calculatedAngleThetaRad = Math.atan(sideB / sideA);
var calculatedAngleThetaDeg = calculatedAngleThetaRad * (180 / Math.PI);
var calculatedAnglePhiDeg = 90 – calculatedAngleThetaDeg; // The other acute angle
resultDiv.innerHTML =
"Calculated Hypotenuse: " + calculatedHypotenuse.toFixed(2) + "" +
"Calculated Angle θ: " + calculatedAngleThetaDeg.toFixed(2) + "°" +
"Calculated Angle φ: " + calculatedAnglePhiDeg.toFixed(2) + "°";
calculated = true;
}
// Case 2: One side and hypotenuse given (calculate other side and angles)
else if (!isNaN(sideA) && isNaN(sideB) && !isNaN(hypotenuse) && isNaN(angleTheta)) {
if (hypotenuse <= sideA) {
resultDiv.innerHTML = "Error: Hypotenuse must be greater than Side A.";
return;
}
var calculatedSideB = Math.sqrt(hypotenuse * hypotenuse – sideA * sideA);
var calculatedAngleThetaRad = Math.asin(calculatedSideB / hypotenuse);
var calculatedAngleThetaDeg = calculatedAngleThetaRad * (180 / Math.PI);
var calculatedAnglePhiDeg = 90 – calculatedAngleThetaDeg;
resultDiv.innerHTML =
"Calculated Side B: " + calculatedSideB.toFixed(2) + "" +
"Calculated Angle θ: " + calculatedAngleThetaDeg.toFixed(2) + "°" +
"Calculated Angle φ: " + calculatedAnglePhiDeg.toFixed(2) + "°";
calculated = true;
}
else if (isNaN(sideA) && !isNaN(sideB) && !isNaN(hypotenuse) && isNaN(angleTheta)) {
if (hypotenuse <= sideB) {
resultDiv.innerHTML = "Error: Hypotenuse must be greater than Side B.";
return;
}
var calculatedSideA = Math.sqrt(hypotenuse * hypotenuse – sideB * sideB);
var calculatedAngleThetaRad = Math.acos(calculatedSideA / hypotenuse);
var calculatedAngleThetaDeg = calculatedAngleThetaRad * (180 / Math.PI);
var calculatedAnglePhiDeg = 90 – calculatedAngleThetaDeg;
resultDiv.innerHTML =
"Calculated Side A: " + calculatedSideA.toFixed(2) + "" +
"Calculated Angle θ: " + calculatedAngleThetaDeg.toFixed(2) + "°" +
"Calculated Angle φ: " + calculatedAnglePhiDeg.toFixed(2) + "°";
calculated = true;
}
// Case 3: One side and an angle given (calculate other side, hypotenuse, and other angle)
else if (!isNaN(sideA) && isNaN(sideB) && isNaN(hypotenuse) && !isNaN(angleTheta)) {
if (angleTheta = 90) {
resultDiv.innerHTML = "Error: Angle θ must be between 0° and 90°.";
return;
}
var angleThetaRad = angleTheta * (Math.PI / 180);
var calculatedSideB = sideA * Math.tan(angleThetaRad);
var calculatedHypotenuse = sideA / Math.cos(angleThetaRad);
var calculatedAnglePhiDeg = 90 – angleTheta;
resultDiv.innerHTML =
"Calculated Side B: " + calculatedSideB.toFixed(2) + "" +
"Calculated Hypotenuse: " + calculatedHypotenuse.toFixed(2) + "" +
"Calculated Angle φ: " + calculatedAnglePhiDeg.toFixed(2) + "°";
calculated = true;
}
else if (isNaN(sideA) && !isNaN(sideB) && isNaN(hypotenuse) && !isNaN(angleTheta)) {
if (angleTheta = 90) {
resultDiv.innerHTML = "Error: Angle θ must be between 0° and 90°.";
return;
}
var angleThetaRad = angleTheta * (Math.PI / 180);
var calculatedSideA = sideB / Math.tan(angleThetaRad);
var calculatedHypotenuse = sideB / Math.sin(angleThetaRad);
var calculatedAnglePhiDeg = 90 – angleTheta;
resultDiv.innerHTML =
"Calculated Side A: " + calculatedSideA.toFixed(2) + "" +
"Calculated Hypotenuse: " + calculatedHypotenuse.toFixed(2) + "" +
"Calculated Angle φ: " + calculatedAnglePhiDeg.toFixed(2) + "°";
calculated = true;
}
// Case 4: Hypotenuse and an angle given (calculate sides and other angle)
else if (isNaN(sideA) && isNaN(sideB) && !isNaN(hypotenuse) && !isNaN(angleTheta)) {
if (angleTheta = 90) {
resultDiv.innerHTML = "Error: Angle θ must be between 0° and 90°.";
return;
}
var angleThetaRad = angleTheta * (Math.PI / 180);
var calculatedSideA = hypotenuse * Math.cos(angleThetaRad);
var calculatedSideB = hypotenuse * Math.sin(angleThetaRad);
var calculatedAnglePhiDeg = 90 – angleTheta;
resultDiv.innerHTML =
"Calculated Side A: " + calculatedSideA.toFixed(2) + "" +
"Calculated Side B: " + calculatedSideB.toFixed(2) + "" +
"Calculated Angle φ: " + calculatedAnglePhiDeg.toFixed(2) + "°";
calculated = true;
}
// Case 5: All values provided, check for consistency
else if (!isNaN(sideA) && !isNaN(sideB) && !isNaN(hypotenuse) && !isNaN(angleTheta)) {
var calculatedHypotenuse = Math.sqrt(sideA * sideA + sideB * sideB);
var calculatedAngleThetaRad = Math.atan(sideB / sideA);
var calculatedAngleThetaDeg = calculatedAngleThetaRad * (180 / Math.PI);
var tolerance = 0.01; // Allow for minor floating point inaccuracies
if (Math.abs(hypotenuse – calculatedHypotenuse) < tolerance &&
Math.abs(angleTheta – calculatedAngleThetaDeg) < tolerance) {
resultDiv.innerHTML = "Provided values are consistent.";
} else {
resultDiv.innerHTML =
"Warning: Provided values are inconsistent." +
"Based on sides A and B, Hypotenuse should be: " + calculatedHypotenuse.toFixed(2) + " and Angle θ should be: " + calculatedAngleThetaDeg.toFixed(2) + "°";
}
calculated = true;
}
if (!calculated) {
resultDiv.innerHTML = "Please provide at least two distinct values (e.g., two sides, or one side and one angle) to perform calculations.";
}
}
Understanding Trigonometry in Geometry
Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. In the context of Common Core Geometry, it's primarily used for right triangles, forming the foundation for more advanced mathematical concepts.
Right Triangles and Their Components
A right triangle is a triangle that has one angle measuring exactly 90 degrees. The sides of a right triangle have specific names relative to the acute angles:
- Hypotenuse: The longest side, always opposite the right angle.
- Opposite Side: The side directly across from a given acute angle (θ).
- Adjacent Side: The side next to the given acute angle (θ), which is not the hypotenuse.
The Six Trigonometric Ratios
For any acute angle θ in a right triangle, there are six trigonometric ratios:
- Sine (sin θ): Opposite / Hypotenuse
- Cosine (cos θ): Adjacent / Hypotenuse
- Tangent (tan θ): Opposite / Adjacent
- Cosecant (csc θ): Hypotenuse / Opposite (1 / sin θ)
- Secant (sec θ): Hypotenuse / Adjacent (1 / cos θ)
- Cotangent (cot θ): Adjacent / Opposite (1 / tan θ)
The Common Core Geometry curriculum typically focuses on the first three: sine, cosine, and tangent.
Using the Calculator
This calculator is designed to help you solve for missing sides or angles in a right triangle when you have enough information. You typically need at least two pieces of information (like two sides, or one side and one angle) to find the rest.
How to use it:
- Enter the known values for the sides (Side A, Side B, Hypotenuse) and the known acute angle (Angle θ) in degrees.
- Leave the fields blank for the values you want the calculator to find.
- Click the "Calculate" button.
The calculator will use the trigonometric ratios and the Pythagorean theorem (a² + b² = c²) to find the unknown values. It's important to ensure your inputs are consistent with the properties of a right triangle.
Example Calculation
Let's say you have a right triangle where:
- Side A (Adjacent to θ) = 3 units
- Side B (Opposite to θ) = 4 units
You want to find the Hypotenuse and Angle θ.
Using the calculator:
- Enter
3 in the "Side A" field.
- Enter
4 in the "Side B" field.
- Leave "Hypotenuse" and "Angle θ" blank.
- Click "Calculate".
Expected Output:
- Calculated Hypotenuse:
5.00 (using Pythagorean theorem: √(3² + 4²) = √25 = 5)
- Calculated Angle θ:
53.13° (using arctan(4/3))
- Calculated Angle φ:
36.87° (90° – 53.13°)
Pythagorean Theorem
The Pythagorean theorem is fundamental for right triangles and 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 calculator implicitly uses it when calculating a missing side if two other sides are known.
Inverse Trigonometric Functions
When you know the ratios of the sides and want to find the angle, you use the inverse trigonometric functions (also called arctangent, arcsine, and arccosine, often written as atan, asin, acos or tan⁻¹, sin⁻¹, cos⁻¹). For example, if tan θ = Opposite / Adjacent, then θ = atan(Opposite / Adjacent).