1. What is a 15-75-90 Triangle?

A 15-75-90 triangle is a right triangle with angles measuring 15°, 75°, and 90°. It's a special triangle with unique side length relationships, though not as commonly known as the 30-60-90 or 45-45-90 triangles.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines:

Where:

• \( a \) — Length of side a
• \( b \) — Length of side b
• \( C \) — 90° angle between sides a and b
• \( c \) — Length of the hypotenuse

Explanation: The formula calculates the third side of any triangle when two sides and the included angle are known.

3. Properties of 15-75-90 Triangles

Details: In a 15-75-90 triangle:

• The sides are in the ratio approximately 1 : 3.732 : 3.864
• The hypotenuse is about 3.864 times the shortest side
• The medium side is about 3.732 times the shortest side

4. Using the Calculator

Tips: Enter lengths for any two sides to calculate the third. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's special about a 15-75-90 triangle?
A: It has angle measures of 15°, 75°, and 90° with side ratios that can be derived using trigonometric functions.

Q2: How does this differ from a 30-60-90 triangle?
A: The 30-60-90 has simpler side ratios (1:√3:2) while the 15-75-90 has more complex ratios involving trigonometric values of 15°.

Q3: Can I use this for any right triangle?
A: Yes, the Law of Cosines works for any triangle, though for right triangles, the Pythagorean theorem is simpler.

Q4: What are practical applications of this triangle?
A: It's useful in trigonometry problems, engineering calculations, and when working with angles of 15° or 75°.

Q5: How accurate are the calculations?
A: The calculator provides precise results based on the input values and mathematical formulas.