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This formula calculates the length of side B in a triangle when you know the lengths of sides A and C, and the measures of angles B and C. It uses trigonometric relationships to determine the missing side length.
The calculator uses the formula:
Where:
Explanation: This formula uses cosine functions to relate the known sides and angles to find the unknown side length in a triangle.
Details: Calculating unknown sides in triangles is fundamental in geometry, trigonometry, and various applied fields such as engineering, architecture, and physics where triangular relationships are common.
Tips: Enter side lengths in meters, angles in radians. All values must be valid (non-negative). Ensure angle values are appropriate for triangle angles (between 0 and π radians).
Q1: Why use radians instead of degrees for angles?
A: Trigonometric functions in mathematical calculations typically use radians. If you have degrees, convert them to radians first (radians = degrees × π/180).
Q2: What if the calculated side length is negative?
A: A negative result may indicate invalid input values that don't form a valid triangle. Check your input values and ensure they satisfy triangle inequality and angle sum properties.
Q3: Can this formula be used for any type of triangle?
A: This specific formula is derived for triangles where two sides and their opposite angles are known. It works for various triangle types but requires appropriate input values.
Q4: What are the limitations of this calculation?
A: The formula assumes valid triangle measurements. Results may be inaccurate or undefined if input values don't correspond to a possible triangle or if cosine values approach zero.
Q5: How precise are the results?
A: The calculator provides results rounded to 10 decimal places, which is typically sufficient for most practical applications involving triangle calculations.