Triangle With 3 Sides Calculator

Cosine Law Formula:

\[ \angle A = \arccos\left(\frac{b^2 + c^2 - a^2}{2 \times b \times c}\right) \]

Angle A:

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1. What Is The Cosine Law?

The Law of Cosines (also known as the Cosine Formula or Cosine Rule) is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is useful for solving triangles when you know all three sides or two sides and the included angle.

2. How Does The Calculator Work?

The calculator uses the Cosine Law formula:

\[ \angle A = \arccos\left(\frac{b^2 + c^2 - a^2}{2 \times b \times c}\right) \]

Where:

\( a \) — Side opposite to angle A
\( b \) — One of the adjacent sides
\( c \) — The other adjacent side
\( \arccos \) — Inverse cosine function

Explanation: The formula calculates the angle opposite to side a using the lengths of all three sides of the triangle.

3. Importance Of Angle Calculation

Details: Calculating angles in triangles is fundamental in geometry, engineering, architecture, and various fields of science. It helps in determining the shape and properties of triangular structures.

4. Using The Calculator

Tips: Enter the lengths of all three sides of the triangle in meters. All values must be positive and must satisfy the triangle inequality theorem (the sum of any two sides must be greater than the third side).

5. Frequently Asked Questions (FAQ)

Q1: What is the triangle inequality theorem?
A: The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is a necessary condition for any valid triangle.

Q2: Can I calculate other angles using this formula?
A: Yes, you can calculate any angle by rearranging the formula. For angle B: \( \angle B = \arccos\left(\frac{a^2 + c^2 - b^2}{2 \times a \times c}\right) \), and for angle C: \( \angle C = \arccos\left(\frac{a^2 + b^2 - c^2}{2 \times a \times b}\right) \).

Q3: What units should I use for the side lengths?
A: The calculator uses meters, but you can use any unit of length as long as you're consistent. The angle result will be the same regardless of the unit.

Q4: What if I get an error message?
A: The error message indicates that the side lengths you entered cannot form a valid triangle. Check your values and ensure they satisfy the triangle inequality theorem.

Q5: How accurate are the results?
A: The results are accurate to two decimal places. The precision depends on the accuracy of your input values and the mathematical implementation of the trigonometric functions.