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Triangle Side Angle Calculator

Triangle Formulas:

\[ \text{Law of Sines: } \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \] \[ \text{Law of Cosines: } c^2 = a^2 + b^2 - 2ab\cos C \]

meters
meters
degrees

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1. What is a Triangle Side Angle Calculator?

Definition: This calculator solves for unknown sides and angles in a triangle when given two sides and the included angle.

Purpose: It helps in trigonometry problems, construction planning, navigation, and various engineering applications.

2. How Does the Calculator Work?

The calculator uses two fundamental trigonometric laws:

\[ \text{Law of Cosines: } c^2 = a^2 + b^2 - 2ab\cos C \] \[ \text{Law of Sines: } \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]

Process:

  1. Calculates the third side (c) using the Law of Cosines
  2. Determines the remaining angles using the Law of Sines
  3. Verifies the angles sum to 180°

3. When to Use This Calculator

Applications:

4. Using the Calculator

Instructions:

  1. Enter the lengths of two sides (a and b) in meters
  2. Enter the included angle (C) between these sides in degrees
  3. Click "Calculate" to get the third side and remaining angles

5. Frequently Asked Questions (FAQ)

Q1: What if I know different elements of the triangle?
A: This calculator specifically solves SAS (Side-Angle-Side) cases. Other versions handle different combinations.

Q2: How accurate are the results?
A: Results are accurate to 3 decimal places for sides and 2 decimal places for angles.

Q3: What units does the calculator use?
A: Sides are in meters, angles in degrees. You can use any consistent units for sides.

Q4: What if my angles don't add up to 180°?
A: The calculator automatically ensures angle sum validity through its calculations.

Q5: Can I use this for right triangles?
A: Yes, though right triangles have simpler formulas (Pythagorean theorem).

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