Calculate sine, cosine, tangent, and right triangle measurements in one place. Solve for missing sides, angles, area, and perimeter in degrees or radians with fast, accurate results.
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This right triangle trigonometry calculator is built for two common jobs: evaluating trig functions and solving right triangles. If you are checking homework, planning a ladder angle, or verifying field measurements, you can move from input to answer in a few quick steps.
Choose Trigonometric Functions when you already know an angle, or switch to Right Triangle when you need missing sides, angles, or area.
Add the angle, the side lengths, or the area values you already have. For triangle problems, you only need a valid combination of measurements.
Use degrees for most geometry, construction, and classroom work. Use radians when your formula, graph, or textbook is based on the unit circle.
Read the result card carefully. It shows the solved value first, then the supporting details so you can check the math and use the answer with confidence.
Start by choosing the function you need: sine, cosine, tangent, cosecant, secant, or cotangent. Then enter the angle and confirm whether the value is in degrees or radians. This matters because `sin(30°)` is not the same input as `sin(30)` in radians.
This is useful when you need fast trig ratios for a graphing task, a physics problem, or a geometry worksheet. It also helps when you are moving between textbook values and decimal approximations.
The right triangle tab is strongest when you know two sides, one acute angle and one side, or the area and one side. Those are the combinations that let the calculator apply SOHCAHTOA and the Pythagorean theorem without guessing.
If you are solving by hand alongside the calculator, label the opposite side, adjacent side, and hypotenuse before you begin. That small step prevents most trigonometry mistakes.
When you use a right triangle trigonometry calculator, the first number you see is usually the value you care about most. On the function tab, that means the trig ratio itself. On the triangle tab, that may be the missing side, one of the acute angles, the area, or the perimeter.
In a right triangle, the hypotenuse should always be the longest side because it sits across from the 90 degree angle. The two acute angles should add up to 90 degrees. Those are the fastest checks to confirm your answer is sensible.
The area result tells you how much two-dimensional space is inside the triangle. The perimeter is the total distance around it. Those outputs matter in framing, trim work, survey sketches, classroom diagrams, and many other everyday geometry tasks.
Decimal rounding matters too. A classroom problem may want exact answers or four decimal places, while a construction estimate may only need a practical rounded measurement.
Right triangle trigonometry uses three main ratios. Sine compares the opposite side to the hypotenuse. Cosine compares the adjacent side to the hypotenuse. Tangent compares the opposite side to the adjacent side. Many students remember this as SOHCAHTOA.
sin(theta) = opposite / hypotenuse
cos(theta) = adjacent / hypotenuse
tan(theta) = opposite / adjacent
hypotenuse = sqrt(a^2 + b^2)
area = 1/2 x base x height
perimeter = a + b + c
To find a missing side, choose the ratio that uses the side you know and the side you want. To find a missing angle, use inverse trig. If you know the opposite side and adjacent side, calculate `theta = arctan(opposite / adjacent)`.
A 20 foot ladder leans against a wall, and the bottom of the ladder is 12 feet from the wall.
Height = sqrt(20^2 - 12^2) = sqrt(256) = 16 feet.
Ground angle = arctan(16 / 12) ≈ 53.13 degrees.
If a ladder is 20 feet long and sits 12 feet from the wall, the ladder reaches 16 feet high and makes a 53.13 degree angle with the ground.
A roof rises 6 feet over a 12 foot run. The slope angle is about 26.57 degrees, and the rafter length is about 13.42 feet.
If a ramp rises 2.5 feet over 30 feet, the angle is about 4.76 degrees.
If you stand 80 feet from a flagpole and the angle of elevation is 32 degrees, the height is about 49.99 feet.
Two special patterns save time in right triangle work. A 45-45-90 triangle has equal legs and a hypotenuse of `x x sqrt(2)`. A 30-60-90 triangle follows the ratio `1 : sqrt(3) : 2`.
These patterns connect directly to the unit circle and to exact trig values like `sin(30°) = 1/2`, `cos(60°) = 1/2`, and `tan(45°) = 1`.
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Get answers to the most common right triangle and trig calculator questions.
Pick the mode that matches your problem, enter the values you already know, choose degrees or radians when needed, and run the calculation.
You usually need either two sides or one acute angle and one side.
Use degrees for most everyday geometry problems and radians for unit-circle or calculus-based work.
Use SOHCAHTOA and rearrange the ratio that matches the side and angle you know.
Use inverse trig such as arcsin, arccos, or arctan when you know two sides.
Because tangent is sine divided by cosine, and cosine equals zero at 90 degrees.
Sine uses opposite over hypotenuse, while cosine uses adjacent over hypotenuse.
Yes. Once one leg is found from the area formula, the rest of the triangle can be solved.