1. What is the Length of Rectangle Given Diagonal and Angle Formula?

The formula calculates the length of a rectangle when the diagonal and the angle between the diagonal and the length are known. It uses trigonometric principles to determine the length dimension.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l \) — Length of Rectangle (m)
• \( d \) — Diagonal of Rectangle (m)
• \( \angle dl \) — Angle between Diagonal and Length of Rectangle (°)

Explanation: The formula applies the cosine function to find the adjacent side (length) in the right triangle formed by the diagonal, length, and width of the rectangle.

3. Importance of Length Calculation

Details: Calculating the length of a rectangle from its diagonal and angle is important in geometry, construction, and various engineering applications where precise dimensions are required.

4. Using the Calculator

Tips: Enter the diagonal measurement in meters and the angle in degrees between 0 and 90. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why use cosine in this formula?
A: Cosine is used because it represents the ratio of the adjacent side (length) to the hypotenuse (diagonal) in a right triangle.

Q2: What is the valid range for the angle?
A: The angle must be between 0° and 90° since it represents an angle in a right triangle.

Q3: Can this formula be used for any rectangle?
A: Yes, this formula applies to all rectangles as long as the diagonal and angle are accurately measured.

Q4: How accurate is this calculation?
A: The accuracy depends on the precision of the input values. The calculator provides results with up to 6 decimal places.

Q5: What units should be used?
A: The calculator uses meters for length and diagonal, and degrees for angle. Ensure consistent units for accurate results.