Right Triangle Angle Calculator
function calculateRightTriangleAngles() {
var sideA_str = document.getElementById("sideA").value;
var sideB_str = document.getElementById("sideB").value;
var hypotenuse_str = document.getElementById("hypotenuse").value;
var valA = parseFloat(sideA_str);
var valB = parseFloat(sideB_str);
var valHypotenuse = parseFloat(hypotenuse_str);
var inputsCount = 0;
if (!isNaN(valA) && valA > 0) inputsCount++;
if (!isNaN(valB) && valB > 0) inputsCount++;
if (!isNaN(valHypotenuse) && valHypotenuse > 0) inputsCount++;
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (inputsCount !== 2) {
resultDiv.innerHTML = "Please enter exactly two positive side lengths.";
return;
}
var angleA_rad, angleB_rad;
var calculatedSide = "";
var calculatedSideName = "";
// Case 1: Side A and Side B are given
if (!isNaN(valA) && !isNaN(valB) && valA > 0 && valB > 0 && isNaN(valHypotenuse)) {
angleA_rad = Math.atan(valA / valB);
angleB_rad = Math.atan(valB / valA);
calculatedSide = Math.sqrt(valA * valA + valB * valB);
calculatedSideName = "Hypotenuse";
}
// Case 2: Side A and Hypotenuse are given
else if (!isNaN(valA) && !isNaN(valHypotenuse) && valA > 0 && valHypotenuse > 0 && isNaN(valB)) {
if (valA >= valHypotenuse) {
resultDiv.innerHTML = "Side A must be shorter than the Hypotenuse.";
return;
}
angleA_rad = Math.asin(valA / valHypotenuse);
angleB_rad = Math.acos(valA / valHypotenuse);
calculatedSide = Math.sqrt(valHypotenuse * valHypotenuse – valA * valA);
calculatedSideName = "Side B";
}
// Case 3: Side B and Hypotenuse are given
else if (!isNaN(valB) && !isNaN(valHypotenuse) && valB > 0 && valHypotenuse > 0 && isNaN(valA)) {
if (valB >= valHypotenuse) {
resultDiv.innerHTML = "Side B must be shorter than the Hypotenuse.";
return;
}
angleB_rad = Math.asin(valB / valHypotenuse);
angleA_rad = Math.acos(valB / valHypotenuse);
calculatedSide = Math.sqrt(valHypotenuse * valHypotenuse – valB * valB);
calculatedSideName = "Side A";
} else {
resultDiv.innerHTML = "Please ensure you enter exactly two positive side lengths and leave the third blank.";
return;
}
var angleA_deg = angleA_rad * (180 / Math.PI);
var angleB_deg = angleB_rad * (180 / Math.PI);
resultDiv.innerHTML += "
Angle A: " + (Math.round(angleA_deg * 100) / 100) + " degrees";
resultDiv.innerHTML += "
Angle B: " + (Math.round(angleB_deg * 100) / 100) + " degrees";
resultDiv.innerHTML += "
" + calculatedSideName + ": " + (Math.round(calculatedSide * 100) / 100) + " units";
resultDiv.innerHTML += "
(Note: Angle C is 90 degrees)";
}
Understanding Right Triangles and Their Angles
A right triangle is a special type of triangle that has one angle measuring exactly 90 degrees. This 90-degree angle is often referred to as the "right angle." The side opposite the right angle is always the longest side and is called the "hypotenuse." The other two sides are known as "legs" or "cathetus."
Key Properties of a Right Triangle:
- One Right Angle: Always 90 degrees.
- Two Acute Angles: The other two angles are always less than 90 degrees.
- Sum of Angles: The sum of all three angles in any triangle, including a right triangle, is always 180 degrees. Therefore, the two acute angles must sum up to 90 degrees.
- Pythagorean Theorem: For a right triangle with legs 'a' and 'b' and hypotenuse 'c', the relationship a² + b² = c² always holds true.
- Trigonometric Ratios (SOH CAH TOA): These ratios relate the angles of a right triangle to the lengths of its sides:
- Sine (SOH): Sine of an angle = Opposite / Hypotenuse
- Cosine (CAH): Cosine of an angle = Adjacent / Hypotenuse
- Tangent (TOA): Tangent of an angle = Opposite / Adjacent
How to Calculate Angles of a Right Triangle
To calculate the unknown angles of a right triangle, you typically need to know the lengths of at least two of its sides. Our calculator uses the inverse trigonometric functions (arcsin, arccos, arctan) to find these angles based on the sides you provide.
Using the Calculator:
Simply input the lengths of any two sides of your right triangle into the corresponding fields. Leave the third field blank. The calculator will then determine the two acute angles (Angle A and Angle B) and the length of the third missing side. Remember that Angle C is always 90 degrees.
Example Scenarios:
Let's consider a right triangle where:
- Scenario 1: You know Side A and Side B.
If Side A = 3 units and Side B = 4 units:
- The calculator will use the tangent function:
tan(A) = Opposite / Adjacent = 3 / 4.
Angle A = arctan(3/4) ≈ 36.87 degrees.Angle B = arctan(4/3) ≈ 53.13 degrees.- The Hypotenuse will be calculated using the Pythagorean theorem:
√(3² + 4²) = √(9 + 16) = √25 = 5 units.
- Scenario 2: You know Side A and the Hypotenuse.
If Side A = 3 units and Hypotenuse = 5 units:
- The calculator will use the sine function:
sin(A) = Opposite / Hypotenuse = 3 / 5.
Angle A = arcsin(3/5) ≈ 36.87 degrees.- It can also find Angle B using cosine:
cos(B) = Adjacent / Hypotenuse = 3 / 5 (where Side A is adjacent to Angle B).
Angle B = arccos(3/5) ≈ 53.13 degrees.- Side B will be calculated:
√(5² - 3²) = √(25 - 9) = √16 = 4 units.
- Scenario 3: You know Side B and the Hypotenuse.
If Side B = 4 units and Hypotenuse = 5 units:
- The calculator will use the sine function:
sin(B) = Opposite / Hypotenuse = 4 / 5.
Angle B = arcsin(4/5) ≈ 53.13 degrees.- It can also find Angle A using cosine:
cos(A) = Adjacent / Hypotenuse = 4 / 5 (where Side B is adjacent to Angle A).
Angle A = arccos(4/5) ≈ 36.87 degrees.- Side A will be calculated:
√(5² - 4²) = √(25 - 16) = √9 = 3 units.
By understanding these fundamental principles and using the calculator, you can easily determine the unknown angles and sides of any right triangle.
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