Triangle Calculator Given Two Sides

Triangle Formulas:

\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \] \[ c^2 = a^2 + b^2 - 2ab \cos C \]

Side c:

Angle A:

Angle B:

Area:

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1. What is the Triangle Calculator?

The Triangle Calculator solves for all sides and angles of a triangle when given two sides and the included angle. It uses the Law of Cosines and Law of Sines to determine the missing measurements.

2. How Does the Calculator Work?

The calculator uses these formulas:

\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \] \[ c^2 = a^2 + b^2 - 2ab \cos C \]

Where:

\( a, b, c \) — Sides of the triangle
\( A, B, C \) — Angles opposite the respective sides

Explanation: The Law of Cosines calculates the third side, then the Law of Sines calculates the remaining angles.

3. Importance of Triangle Calculations

Details: These calculations are fundamental in geometry, trigonometry, navigation, engineering, and physics for solving real-world problems involving triangular relationships.

4. Using the Calculator

Tips: Enter two side lengths and the included angle in degrees. All values must be positive, and the angle must be between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What if I know two sides and a non-included angle?
A: This calculator is for the included angle case. The non-included angle case may have two, one, or no solutions.

Q2: What units should I use?
A: Any consistent units for length (cm, m, inches, etc.). Angles must be in degrees.

Q3: Does this work for right triangles?
A: Yes, but right triangles can be solved more simply with Pythagorean theorem and basic trig functions.

Q4: What about obtuse triangles?
A: The calculator works for all triangle types (acute, right, obtuse) as long as the angle is less than 180°.

Q5: How accurate are the results?
A: Results are accurate to two decimal places, sufficient for most practical applications.