Example Data Table
| Case |
Known side a |
Known side b |
Known c |
Known angle A |
Expected use |
| Two legs |
3 |
4 |
|
|
Find hypotenuse and angles |
| Leg and hypotenuse |
5 |
|
13 |
|
Find missing leg and angles |
| Angle and hypotenuse |
|
|
10 |
30 |
Find both legs |
| Angle and adjacent side |
|
12 |
|
40 |
Find opposite side and hypotenuse |
Formula Used
The calculator uses the Pythagorean theorem for side relationships.
c = sqrt(a² + b²)
When the hypotenuse and one leg are known, the missing leg is found by subtraction inside the square root.
a = sqrt(c² - b²) and b = sqrt(c² - a²)
Trigonometric ratios connect each acute angle with side lengths.
sin(A) = a / c, cos(A) = b / c, and tan(A) = a / b
The area is (a × b) / 2. The perimeter is a + b + c.
The altitude to the hypotenuse is (a × b) / c. The inradius is (a + b - c) / 2.
How to Use This Calculator
Enter two known values. Leave the unknown boxes empty. Use side a for the side opposite angle A. Use side b for the side beside angle A. Use side c for the hypotenuse. Enter acute angles in degrees only. Select the decimal places you want. Add a unit label if needed. Press the calculate button. The answer will appear below the header and above the form. Use the CSV or PDF button to save the final result.
Right Triangle Trigonometry Guide
Why this tool helps
A right triangle has one angle equal to ninety degrees. That fixed angle makes the triangle predictable. When two independent values are known, the remaining parts can be found. This calculator supports common classroom and field cases. You may enter two sides. You may also enter one acute angle and one side. The tool then returns missing sides, acute angles, area, perimeter, and useful ratios.
What the values mean
Side a is opposite angle A. Side b is adjacent to angle A. Side c is the hypotenuse. The hypotenuse is always the longest side. Angle A and angle B are the two acute angles. They always add to ninety degrees. These names help the formulas stay clear. They also make the result table easier to read.
Practical uses
Students can check homework steps with quick feedback. Builders can estimate rise, run, and slope. Designers can convert a measured angle into a needed length. Survey notes can be tested before a drawing is finalized. The extra values are helpful too. Area shows covered space. Perimeter gives total edge length. Trigonometric ratios show the relationship between sides.
Accuracy and limits
The calculator uses standard right triangle formulas. Results are rounded for readable output. Small decimal differences may appear after rounding. Measurements should use the same unit. Do not mix inches and feet unless you convert first. Angles should be entered in degrees. Acute angles must be greater than zero and less than ninety. If all three sides are entered, the tool checks whether they satisfy the right triangle rule.
Best workflow
Start with the values you trust most. Leave unknown fields blank. Enter two independent values only when possible. Press calculate and review the solving steps. Compare the sides with the diagram labels. Export the result when you need a record. Use the example table to understand typical entries. Repeat with new values whenever the problem changes.
For stronger learning, read the ratios beside the side lengths. Sine compares opposite side and hypotenuse. Cosine compares adjacent side and hypotenuse. Tangent compares opposite and adjacent sides. These ratios connect geometry with angle measurement and problem solving. They form a base for later trigonometry topics too.
FAQs
What values can I enter?
You can enter two sides, or one side with one acute angle. Leave unknown fields blank. The tool solves the remaining right triangle values automatically.
What is side c?
Side c is the hypotenuse. It sits opposite the right angle. It must be the longest side in a valid right triangle.
Can I enter both acute angles?
Yes, but they must add to ninety degrees. One side is still needed to find actual side lengths, area, and perimeter.
What happens if I enter all three sides?
The calculator checks the Pythagorean rule. If the sides do not fit a right triangle, it shows an input warning.
Are angles entered in radians?
No. Enter angles in degrees. The calculator converts them internally when it applies sine, cosine, tangent, and inverse trigonometric functions.
Can I use feet or inches?
Yes. Use any unit, but keep every side in the same unit. The unit label is printed beside length results.
Why are results rounded?
Rounding keeps the output readable. You can choose the decimal places field to show fewer or more digits in the final tables.
Does this replace a geometry lesson?
No. It supports learning and checking. Read the formula section and steps to understand how each result is produced.