Side A of Triangle given Two Sides and Two Angles A and C Calculator

Formula Used:

\[ Sa = \frac{Sb - Sc \times \cos(\angle A)}{\cos(\angle C)} \]

Side B of Triangle:

Meter

Side C of Triangle:

Meter

Angle A of Triangle:

Degree

Angle C of Triangle:

Degree

Side A of Triangle:

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1. What is the Side A of Triangle Formula?

The formula calculates the length of side A of a triangle when given sides B and C, and angles A and C. This trigonometric approach uses the cosine function to determine the unknown side length based on the given measurements.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Sa = \frac{Sb - Sc \times \cos(\angle A)}{\cos(\angle C)} \]

Where:

\( Sa \) — Side A of Triangle (Meter)
\( Sb \) — Side B of Triangle (Meter)
\( Sc \) — Side C of Triangle (Meter)
\( \angle A \) — Angle A of Triangle (Radian)
\( \angle C \) — Angle C of Triangle (Radian)

Explanation: The formula uses trigonometric cosine functions to calculate the unknown side length based on the relationship between the given sides and angles in the triangle.

3. Importance of Triangle Side Calculation

Details: Calculating unknown sides of triangles is fundamental in geometry, engineering, architecture, and various scientific applications where precise measurements and spatial relationships are crucial.

4. Using the Calculator

Tips: Enter side lengths in meters and angles in degrees. All values must be positive numbers. Angles should be between 0 and 180 degrees for valid triangle angles.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the inputs?
A: Side lengths should be in meters and angles in degrees. The calculator automatically converts degrees to radians for trigonometric calculations.

Q2: Can this formula be used for any type of triangle?
A: This specific formula is designed for triangles where sides B, C and angles A, C are known. It may not be applicable to all triangle configurations.

Q3: What if I get a negative result?
A: A negative result typically indicates that the input values do not form a valid triangle. Please verify your measurements.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values. The accuracy depends on the precision of your input measurements.

Q5: Can this be used for real-world applications?
A: Yes, this formula is commonly used in surveying, navigation, construction, and other fields where triangle geometry calculations are required.