Triangle Sin Cos Tan Calculator

Calculator Form

Calculation Method

Unit Label

Side a / Opposite

Side b / Adjacent

Side c / Hypotenuse

Angle A Degrees

Angle B Degrees

Example Data Table

Method	Inputs	Expected Use
Three sides	a = 3, b = 4, c = 5	Find all angles and ratios.
Right: hypotenuse and angle	c = 10, A = 30°	Find opposite, adjacent, and ratios.
Side b, side c, included angle A	b = 8, c = 6, A = 60°	Solve a general triangle.
Angle A, angle B, side a	A = 45°, B = 65°, a = 12	Use angle sum and law of sines.

Formulas Used

Right triangle theorem: a² + b² = c².

Sine ratio: sin(A) = opposite / hypotenuse.

Cosine ratio: cos(A) = adjacent / hypotenuse.

Tangent ratio: tan(A) = opposite / adjacent.

Law of cosines: a² = b² + c² - 2bc cos(A).

Law of sines: a / sin(A) = b / sin(B) = c / sin(C).

Angle sum: A + B + C = 180°.

Heron area: Area = √s(s - a)(s - b)(s - c), where s = (a + b + c) / 2.

How to Use This Calculator

Select the method that matches your known values.
Enter only the values required for that method.
Use degrees for every angle field.
Use one unit type for all side values.
Press the calculate button.
Review sides, angles, area, perimeter, sine, cosine, and tangent.
Use the CSV or PDF button after a result appears.

Triangle Ratio Calculator Guide

What This Tool Does

This triangle calculator helps you study sides, angles, and trigonometric ratios in one place. It supports right triangle work and general triangle work. You can enter three sides, two sides with an included angle, or angle based right triangle data. The tool then estimates missing measures and shows sine, cosine, and tangent values for each angle.

Why Ratios Matter

Sine, cosine, and tangent connect an angle with side lengths. These ratios make triangle problems easier. They are used in surveying, construction, physics, mapping, gaming, navigation, and classroom geometry. A ratio also checks whether a triangle solution looks reasonable. When one angle grows, its opposite side usually grows too.

Main Calculation Ideas

For right triangles, the calculator can use the Pythagorean theorem. It can also use SOH CAH TOA. Sine is opposite divided by hypotenuse. Cosine is adjacent divided by hypotenuse. Tangent is opposite divided by adjacent. For general triangles, it can use the law of cosines, the law of sines, Heron's formula, and the angle sum rule.

Practical Uses

Students can verify homework steps. Teachers can create quick examples. Designers can estimate slopes. Builders can compare diagonal braces. Hobbyists can calculate ramps, roof pitch, model parts, or game map distances. The CSV export keeps a spreadsheet record. The PDF export gives a clean printable summary.

Accuracy Tips

Use the same unit for every side. Degrees are expected for angles. Avoid rounded inputs when possible. Very small angles can create large tangent values. Invalid triangles are rejected, because the sum of two sides must be greater than the third side. Angle totals should also fit normal triangle rules. Check the notes beside the output before using results in real projects.

Best Workflow

Start with the most reliable measurements. Choose the matching solve method. Enter values only in the fields required by that method. Press calculate. Review sides, angles, area, perimeter, and all trigonometric ratios. Then export the result if you need documentation. This process reduces errors and keeps each triangle calculation clear, traceable, and easy to repeat. Because the page stores the latest result in fields, downloads match the visible answer and help prevent copied numbers from drifting during later reviews or edits.

FAQs

1. What does side a mean?

Side a is opposite angle A. Side b is opposite angle B. Side c is opposite angle C. In right triangle modes, side c is treated as the hypotenuse.

2. Can I use any unit?

Yes. You can use centimeters, meters, inches, feet, or another unit. Use the same unit for all sides. The calculator keeps area in square units.

3. Should angles be entered in radians?

No. Enter all angles in degrees. The calculator converts degrees internally before applying sine, cosine, tangent, and inverse trigonometric calculations.

4. Why is tangent sometimes undefined?

Tangent equals sine divided by cosine. At 90 degrees, cosine is zero. Division by zero is not defined, so the result is shown as undefined.

5. What is the best method for a right triangle?

Choose the method matching your known data. Use two legs, hypotenuse with angle, adjacent with angle, opposite with angle, or hypotenuse with one leg.

6. Why does the calculator reject some side values?

A real triangle must pass the triangle inequality rule. The sum of any two sides must be greater than the third side.

7. What does the CSV button do?

It downloads the latest result in spreadsheet format. You can open it in common spreadsheet tools and store calculations for later comparison.

8. Is this suitable for engineering work?

It is useful for checking triangle math. For final engineering decisions, confirm measurements, tolerances, safety rules, and professional standards before applying results.