Triangle Calculator Square Root

This triangle calculator helps you find missing sides, angles, and area of right triangles using square roots. Whether you're solving geometry problems or verifying construction measurements, this tool provides accurate results with clear explanations.

How to Use This Calculator

To use the triangle calculator square root, follow these steps:

Select the type of triangle you're working with (right triangle or general triangle).
Enter the known values in the appropriate fields.
Click "Calculate" to see the results.
Review the solution and formulas used.

The calculator will automatically determine which values to solve for based on the inputs you provide.

Formulas Used

Right Triangle Formulas

For right triangles, we use the Pythagorean theorem:

a² + b² = c²

Where c is the hypotenuse, and a and b are the other two sides.

General Triangle Formulas

For non-right triangles, we use the Law of Cosines:

c² = a² + b² - 2ab cos(C)

And the Law of Sines:

a/sin(A) = b/sin(B) = c/sin(C)

These formulas allow us to solve for missing sides and angles when we know at least two sides and one angle, or three sides.

Worked Examples

Example 1: Right Triangle

Given a right triangle with sides a = 3 and b = 4, find the hypotenuse c.

Using the Pythagorean theorem:

c = √(a² + b²) = √(3² + 4²) = √(9 + 16) = √25 = 5

The hypotenuse is 5 units long.

Example 2: General Triangle

Given a triangle with sides a = 5, b = 7, and angle C = 60°, find side c.

Using the Law of Cosines:

c² = a² + b² - 2ab cos(C) = 25 + 49 - 2×5×7×0.5 = 74 - 35 = 39

c = √39 ≈ 6.245

The missing side is approximately 6.245 units long.

Frequently Asked Questions

What types of triangles can this calculator solve?: This calculator can solve right triangles and general triangles using the Pythagorean theorem and trigonometric laws.
How accurate are the calculations?: The calculator uses precise mathematical formulas and JavaScript's built-in square root function to provide accurate results.
Can I use this calculator for construction measurements?: Yes, this calculator is useful for verifying construction measurements, especially when dealing with right triangles.
What if I don't know any angles?: If you only know the sides of a triangle, the calculator will use the Law of Cosines to find the angles.
Is there a mobile app version of this calculator?: Currently, this is a web-based calculator that works on all devices. We may develop a mobile app in the future.