Triangle Calculator with Angle and Side

Law of Sines Formula:

\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]

Other Side Length (m):

Third Angle (°):

Third Side Length (m):

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1. What is a Triangle Calculator with Angle and Side?

Definition: This calculator solves triangle dimensions using the Law of Sines when you know one side length and two angles.

Purpose: It helps in trigonometry problems, construction planning, and any application requiring triangle measurements.

2. How Does the Calculator Work?

The calculator uses the Law of Sines formula:

\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]

Where:

\( a, b, c \) — Side lengths of the triangle
\( A, B, C \) — Angles opposite those sides respectively

Explanation: Given one side and its opposite angle, plus another angle, we can calculate all remaining sides and angles.

3. Importance of Triangle Calculations

Details: Accurate triangle calculations are essential in construction, navigation, engineering, and various scientific applications.

4. Using the Calculator

Tips: Enter the known side length (meters), known angle (degrees), and another angle (degrees). All angles must sum to less than 180°.

5. Frequently Asked Questions (FAQ)

Q1: What if my angles sum to 180° or more?
A: The calculator won't compute as this would violate the triangle angle sum theorem (angles must sum to exactly 180°).

Q2: Can I use this for right triangles?
A: Yes, though right triangles can also be solved with simpler Pythagorean theorem when appropriate.

Q3: What units does this calculator use?
A: Side lengths are in meters, angles in degrees. You can convert results as needed.

Q4: How accurate are the results?
A: Results are mathematically precise, though practical measurements may have real-world variations.

Q5: What if I know two sides and an angle?
A: For that case, you would need a different calculator using the Law of Cosines.