Right Triangle Calculator with Coordinates

Right Triangle Properties:

\[ \text{Hypotenuse} = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \] \[ \text{Area} = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2 \] \[ \text{Perimeter} = \text{leg}_1 + \text{leg}_2 + \text{hypotenuse} \]

Leg 1:

Leg 2:

Hypotenuse:

Area:

Perimeter:

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1. What is a Right Triangle?

A right triangle is a triangle with one angle exactly 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called legs. The Pythagorean theorem relates these sides: \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse.

2. How the Calculator Works

The calculator uses coordinate geometry to determine if three points form a right triangle and calculates its properties:

\[ \text{Distance between points} = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \] \[ \text{Area} = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2 \] \[ \text{Perimeter} = \text{leg}_1 + \text{leg}_2 + \text{hypotenuse} \]

Steps:

Calculate distances between all three points
Check if they satisfy the Pythagorean theorem
If valid, calculate area and perimeter

3. Using the Calculator

Instructions: Enter the (x,y) coordinates of three points in the plane. The calculator will determine if they form a right triangle and calculate all properties if they do.

4. Practical Applications

Applications: Right triangle calculations are used in construction, navigation, computer graphics, and many engineering fields where precise angle and distance measurements are needed.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is this calculator?
A: The calculator uses floating-point arithmetic with about 15 digits of precision, but displays results rounded to 2 decimal places.

Q2: What if my points don't form a right triangle?
A: The calculator will display an error message indicating the points don't form a right triangle.

Q3: Can I use negative coordinates?
A: Yes, the calculator works with any real number coordinates in the Cartesian plane.

Q4: How are the legs and hypotenuse identified?
A: The calculator sorts the sides by length and applies the Pythagorean theorem to the two shorter sides and the longest side.

Q5: What units does this calculator use?
A: The calculator assumes all coordinates are in the same units (e.g., meters), and results are given in those units.