Angle of Right Triangle Calculator

Right Triangle Angle Calculator

function calculateRightTriangleAngles() { var legA_str = document.getElementById('legA').value; var legB_str = document.getElementById('legB').value; var hypotenuse_str = document.getElementById('hypotenuse').value; var legA = parseFloat(legA_str); var legB = parseFloat(legB_str); var hypotenuse = parseFloat(hypotenuse_str); var inputsProvided = 0; if (!isNaN(legA) && legA > 0) inputsProvided++; if (!isNaN(legB) && legB > 0) inputsProvided++; if (!isNaN(hypotenuse) && hypotenuse > 0) inputsProvided++; var resultDiv = document.getElementById('result'); resultDiv.style.color = '#333'; // Reset color for new calculations if (inputsProvided 0 && !isNaN(legB) && legB > 0) { hypotenuse = Math.sqrt(legA * legA + legB * legB); angleA_rad = Math.atan(legA / legB); angleB_rad = Math.atan(legB / legA); } // Case 2: Leg A and Hypotenuse are given else if (!isNaN(legA) && legA > 0 && !isNaN(hypotenuse) && hypotenuse > 0) { if (legA >= hypotenuse) { resultDiv.innerHTML = "Error: Leg A cannot be greater than or equal to the Hypotenuse."; resultDiv.style.color = 'red'; return; } legB = Math.sqrt(hypotenuse * hypotenuse – legA * legA); angleA_rad = Math.asin(legA / hypotenuse); angleB_rad = Math.acos(legA / hypotenuse); // Or Math.asin(legB / hypotenuse) } // Case 3: Leg B and Hypotenuse are given else if (!isNaN(legB) && legB > 0 && !isNaN(hypotenuse) && hypotenuse > 0) { if (legB >= hypotenuse) { resultDiv.innerHTML = "Error: Leg B cannot be greater than or equal to the Hypotenuse."; resultDiv.style.color = 'red'; return; } legA = Math.sqrt(hypotenuse * hypotenuse – legB * legB); angleB_rad = Math.asin(legB / hypotenuse); angleA_rad = Math.acos(legB / hypotenuse); // Or Math.asin(legA / hypotenuse) } else { resultDiv.innerHTML = "Please provide two valid side lengths."; resultDiv.style.color = 'red'; return; } var angleA_deg = angleA_rad * (180 / Math.PI); var angleB_deg = angleB_rad * (180 / Math.PI); // Round values for display legA = legA.toFixed(4); legB = legB.toFixed(4); hypotenuse = hypotenuse.toFixed(4); angleA_deg = angleA_deg.toFixed(4); angleB_deg = angleB_deg.toFixed(4); resultDiv.innerHTML = `

Calculated Right Triangle Properties:

Leg A: ${legA} Leg B: ${legB} Hypotenuse: ${hypotenuse} Angle A: ${angleA_deg}° Angle B: ${angleB_deg}° Angle C (Right Angle): ${angleC_deg}° `; }

Understanding the Right Triangle Angle Calculator

A right triangle is a fundamental shape in geometry, defined by having one angle that measures exactly 90 degrees (a right angle). The side opposite the right angle is called the hypotenuse, and it is always the longest side. The other two sides are called legs.

This calculator helps you determine the unknown angles and sides of a right triangle when you provide at least two known side lengths. This is incredibly useful in various fields, from construction and engineering to navigation and physics.

The Basics of Right Triangles and Trigonometry

The relationships between the sides and angles of a right triangle are governed by trigonometric ratios: sine (sin), cosine (cos), and tangent (tan). These ratios are often remembered by the acronym SOH CAH TOA:

• SOH: Sin(Angle) = Opposite / Hypotenuse
• CAH: Cos(Angle) = Adjacent / Hypotenuse
• TOA: Tan(Angle) = Opposite / Adjacent

To find an angle when you know the side lengths, you use the inverse trigonometric functions: arcsin (sin^-1), arccos (cos^-1), and arctan (tan^-1).

The Pythagorean theorem also plays a crucial role: a² + b² = c², where 'a' and 'b' are the lengths of the legs, and 'c' is the length of the hypotenuse.

How to Use the Calculator

To use the Right Triangle Angle Calculator, simply input the lengths of any two sides of your right triangle. The calculator will then automatically determine the third side and the two acute angles (Angle A and Angle B).

• Leg A: The side opposite Angle A.
• Leg B: The side opposite Angle B.
• Hypotenuse: The longest side, opposite the 90-degree angle.

You only need to fill in two of the three fields. For example, if you know the lengths of Leg A and Leg B, enter those values and leave the Hypotenuse field blank. The calculator will then compute the Hypotenuse and both acute angles.

Formulas Used in the Calculator

The calculator employs the following principles:

1. Pythagorean Theorem: If two legs (a, b) are known, c = √(a² + b²). If a leg (a) and hypotenuse (c) are known, b = √(c² - a²).
2. Inverse Tangent (Arctan): If both legs (a, b) are known:
   • Angle A = arctan(Leg A / Leg B)
   • Angle B = arctan(Leg B / Leg A)
3. Inverse Sine (Arcsin) and Inverse Cosine (Arccos): If a leg (a) and hypotenuse (c) are known:
   • Angle A = arcsin(Leg A / Hypotenuse)
   • Angle B = arccos(Leg A / Hypotenuse) (or arcsin(Leg B / Hypotenuse) once Leg B is found)

All calculated angles are converted from radians to degrees for easier understanding, as 1 radian = 180/π degrees.

Examples

Example 1: Knowing Both Legs

Imagine you have a right triangle where Leg A is 3 units long and Leg B is 4 units long.

• Input: Leg A = 3, Leg B = 4
• Calculation:
  • Hypotenuse = √(3² + 4²) = √(9 + 16) = √25 = 5
  • Angle A = arctan(3/4) ≈ 36.87°
  • Angle B = arctan(4/3) ≈ 53.13°
• Result: Hypotenuse = 5, Angle A ≈ 36.87°, Angle B ≈ 53.13°, Angle C = 90°

Example 2: Knowing One Leg and the Hypotenuse

Consider a right triangle with Leg A measuring 5 units and the Hypotenuse measuring 13 units.

• Input: Leg A = 5, Hypotenuse = 13
• Calculation:
  • Leg B = √(13² – 5²) = √(169 – 25) = √144 = 12
  • Angle A = arcsin(5/13) ≈ 22.62°
  • Angle B = arccos(5/13) ≈ 67.38°
• Result: Leg B = 12, Angle A ≈ 22.62°, Angle B ≈ 67.38°, Angle C = 90°

This calculator simplifies complex trigonometric calculations, making it easy to find the angles and missing sides of any right triangle quickly and accurately.