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The formula calculates the hypotenuse of a right-angled triangle using the adjacent side and the angle alpha. It is derived from the cosine trigonometric function which relates the adjacent side to the hypotenuse.
The calculator uses the formula:
Where:
Explanation: The cosine of an angle in a right triangle is defined as the ratio of the adjacent side to the hypotenuse. Rearranging this relationship gives us the formula to calculate the hypotenuse.
Details: Calculating the hypotenuse is fundamental in trigonometry and has applications in various fields including engineering, architecture, physics, and navigation. It helps in determining distances and relationships between sides in right-angled triangles.
Tips: Enter the adjacent side length in meters and the angle alpha in degrees (must be between 0 and 90 degrees). Both values must be positive numbers.
Q1: Why use cosine function for this calculation?
A: The cosine function specifically relates the adjacent side to the hypotenuse in a right triangle, making it the appropriate trigonometric ratio for this calculation.
Q2: What is the range of valid angle values?
A: Angle alpha must be between 0 and 90 degrees (exclusive) for the calculation to be valid in a right triangle.
Q3: Can this formula be used for any triangle?
A: No, this formula specifically applies to right-angled triangles where one angle is exactly 90 degrees.
Q4: What if the angle is 90 degrees?
A: If the angle is 90 degrees, the cosine becomes 0, and division by zero is undefined. This represents a degenerate case where the adjacent side would be 0.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on trigonometric principles. The practical accuracy depends on the precision of the input measurements.