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90 Degree Triangle Angle Calculator

Angle Formula:

\[ θ = 90° - \arctan\left(\frac{opp}{adj}\right) \]

meters
meters

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1. What is a 90 Degree Triangle Angle Calculator?

Definition: This calculator determines the unknown angle in a right-angled triangle when given the lengths of the opposite and adjacent sides.

Purpose: It helps students, engineers, and construction professionals quickly calculate angles in right triangles for various applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ θ = 90° - \arctan\left(\frac{opp}{adj}\right) \]

Where:

Explanation: The arctangent of the opposite/adjacent ratio gives one acute angle, and subtracting from 90° gives the other acute angle.

3. Importance of Right Triangle Angle Calculation

Details: Accurate angle calculation is essential in construction, engineering, navigation, and various STEM applications involving right triangles.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides in meters. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if I know the hypotenuse instead?
A: Use different trigonometric functions: θ = arcsin(opp/hyp) or θ = arccos(adj/hyp).

Q2: Can I use different units besides meters?
A: Yes, as long as both sides use the same unit, the angle result will be correct.

Q3: How accurate are the results?
A: Results are accurate to two decimal places, sufficient for most practical applications.

Q4: What if my triangle isn't right-angled?
A: This calculator only works for right-angled triangles. Use the Law of Cosines for other triangles.

Q5: Why does the calculator give θ instead of the first calculated angle?
A: By convention, θ represents the unknown angle we're solving for, which is the complement of the arctangent result.

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