Calculate The Size Of Angle X

Triangle Angle Calculation:

\[ \theta = 180° - (\theta_1 + \theta_2) \]

or using cosine rule:

\[ \cos(\theta) = \frac{a^2 + b^2 - c^2}{2ab} \]

Calculation Method:

First Known Angle (θ₁):

degrees

Second Known Angle (θ₂):

degrees

Angle X (θ):

1. Triangle Angle Calculation Methods

There are two main methods to calculate an unknown angle in a triangle: using the sum of angles property (when two angles are known) or using the cosine rule (when all three sides are known).

2. Using Two Known Angles

The simplest method when two angles are known:

\[ \theta = 180° - (\theta_1 + \theta_2) \]

Where:

\( \theta \) — Unknown angle to calculate
\( \theta_1 \) — First known angle
\( \theta_2 \) — Second known angle

Note: The sum of all three angles in any triangle always equals 180°.

3. Using Three Sides (Cosine Rule)

When all three sides are known, use the cosine rule:

\[ \cos(\theta) = \frac{a^2 + b^2 - c^2}{2ab} \]

Where:

\( \theta \) — Angle opposite side c
\( a, b \) — Other two sides of the triangle
\( c \) — Side opposite the angle you're calculating

Note: The sides must satisfy the triangle inequality (sum of any two sides must be greater than the third).

4. Using the Calculator

Method 1 (Two Angles): Enter two known angles (must sum to less than 180°).
Method 2 (Three Sides): Enter all three side lengths (must satisfy triangle inequality).

5. Frequently Asked Questions (FAQ)

Q1: Why does the sum of angles equal 180°?
A: This is a fundamental property of Euclidean triangles. The sum is constant regardless of triangle shape.

Q2: When should I use the cosine rule?
A: Use it when you know all three sides of the triangle or when you know two sides and the included angle.

Q3: What if my angles sum to more than 180°?
A: You've made an error in measurement. In Euclidean geometry, this isn't possible for a triangle.

Q4: Can I use this for non-triangle polygons?
A: No, these methods only work for triangles. For n-sided polygons, the sum of interior angles is (n-2) × 180°.

Q5: How accurate are these calculations?
A: The calculations are mathematically exact. Any inaccuracy comes from measurement errors in your inputs.