1. What is an Obtuse Scalene Triangle?

An obtuse scalene triangle is a triangle with one angle greater than 90° and all sides of different lengths. It combines properties of both obtuse triangles (one angle > 90°) and scalene triangles (no equal sides or angles).

2. How Does the Calculator Work?

The calculator uses the cosine rule:

Where:

• \( a, b, c \) — Lengths of the triangle sides
• \( C \) — Angle opposite side c

Explanation: The formula calculates the cosine of angle C. If cos(C) is negative, the angle is obtuse (between 90° and 180°). The calculator also computes other properties like area and remaining angles.

3. Importance of Triangle Calculations

Details: Understanding triangle properties is essential in geometry, trigonometry, engineering, architecture, and various scientific applications where triangular relationships are fundamental.

4. Using the Calculator

Tips: Enter all three side lengths in the same units. The calculator will verify if the sides form a valid triangle and if it's obtuse. Results include angle measures and area.

5. Frequently Asked Questions (FAQ)

Q1: What makes a triangle obtuse?
A: A triangle is obtuse if one of its angles is greater than 90°. This occurs when the square of the longest side is greater than the sum of squares of the other two sides.

Q2: What's the difference between scalene and other triangles?
A: Scalene triangles have all sides and angles of different measures, unlike isosceles (two equal sides) or equilateral (all sides equal) triangles.

Q3: Can a triangle have more than one obtuse angle?
A: No, the sum of angles in any triangle is 180°, so only one angle can be greater than 90°.

Q4: What if my sides don't form a valid triangle?
A: The calculator checks the triangle inequality theorem (sum of any two sides must be greater than the third). Invalid inputs will show an error.

Q5: How is the area calculated?
A: The area is calculated using Heron's formula: \( \sqrt{s(s-a)(s-b)(s-c)} \) where \( s = \frac{a+b+c}{2} \).