Solve for a Right Triangle Calculator

Right Triangle Formulas:

\[ c = \sqrt{a^2 + b^2} \] \[ \theta = \arctan\left(\frac{b}{a}\right) \]

Hypotenuse (c): meters

Angle (θ): degrees

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1. What is a Right Triangle Calculator?

Definition: This calculator solves for the hypotenuse and angle of a right triangle given the lengths of the two perpendicular sides.

Purpose: It helps students, engineers, and construction professionals quickly solve right triangle problems without manual calculations.

2. How Does the Calculator Work?

The calculator uses the Pythagorean theorem and trigonometric functions:

\[ c = \sqrt{a^2 + b^2} \] \[ \theta = \arctan\left(\frac{b}{a}\right) \]

Where:

\( a \) — Length of adjacent side (meters)
\( b \) — Length of opposite side (meters)
\( c \) — Length of hypotenuse (meters)
\( \theta \) — Angle opposite side b (degrees)

Explanation: The hypotenuse is calculated using the Pythagorean theorem, while the angle is found using the arctangent of the opposite/adjacent ratio.

3. Importance of Right Triangle Calculations

Details: Right triangle calculations are fundamental in construction, navigation, engineering, and physics for determining distances and angles.

4. Using the Calculator

Tips: Enter the lengths of the two perpendicular sides (a and b). All values must be > 0. The calculator will output the hypotenuse length and the angle opposite side b.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: The calculator works with any consistent units (meters, feet, etc.), but outputs will be in the same units as inputs.

Q2: Can I calculate area with this?
A: While not directly shown, area can be calculated as (a × b)/2 using the input values.

Q3: What if I know the hypotenuse and one side?
A: This version requires two perpendicular sides. A future version may include that functionality.

Q4: How precise are the calculations?
A: Results are precise to 3 decimal places for lengths and 2 decimal places for angles.

Q5: Does this work for non-right triangles?
A: No, this calculator is specifically for right triangles only.