Calculate Angles In Right Triangle

Right Triangle Angle Formula:

\[ \theta = \arctan\left(\frac{\text{opposite}}{\text{adjacent}}\right) \]

Angle (radians):

Angle (degrees):

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1. Right Triangle Angle Calculation

The right triangle angle calculator determines an angle using the arctangent of the ratio between the opposite and adjacent sides. This is one of the fundamental trigonometric relationships in right triangles.

2. How the Calculator Works

The calculator uses the arctangent function:

\[ \theta = \arctan\left(\frac{\text{opposite}}{\text{adjacent}}\right) \]

Where:

\( \theta \) — Angle in radians
opposite — Length of side opposite the angle
adjacent — Length of side adjacent to the angle

Explanation: The arctangent function returns the angle whose tangent is the ratio of the opposite side to the adjacent side.

3. Importance of Angle Calculation

Details: Calculating angles in right triangles is essential in geometry, trigonometry, engineering, physics, and many practical applications like construction and navigation.

4. Using the Calculator

Tips: Enter positive values for both the opposite and adjacent sides. The calculator will return the angle in both radians and degrees.

5. Frequently Asked Questions (FAQ)

Q1: What if I know the hypotenuse instead?
A: You can use arcsine (opposite/hypotenuse) or arccosine (adjacent/hypotenuse) depending on which sides you know.

Q2: What units should I use?
A: Any consistent units (cm, m, inches, etc.) as long as both sides use the same units.

Q3: What's the range of possible angles?
A: In a right triangle, the non-right angles range between 0° and 90° (0 to π/2 radians).

Q4: Can I calculate the other angle?
A: Yes, the other non-right angle is 90° minus the calculated angle (π/2 minus the angle in radians).

Q5: What if I enter zero for either side?
A: The calculator requires positive values for both sides as zero would make the triangle degenerate.