Sin Cos Tan Calculator Triangle Without Angles Given

This calculator helps you find the sine, cosine, and tangent values for a triangle when you know the lengths of all three sides, but not the angles. The calculator uses the Law of Cosines and Law of Sines to determine the trigonometric values without needing angle measurements.

How to Use This Calculator

To use this calculator, follow these steps:

Enter the lengths of all three sides of the triangle in the input fields.
Select which trigonometric function you want to calculate (sine, cosine, or tangent).
Click the "Calculate" button to see the results.
Review the results and the visual representation of the triangle.

The calculator will display the sine, cosine, and tangent values for the selected side of the triangle. The results are calculated using the Law of Cosines to find the angles first, then applying the trigonometric functions to those angles.

Formula Used

The calculator uses the following formulas to determine the trigonometric values:

// Law of Cosines to find angle A angleA = acos((b² + c² - a²) / (2 * b * c)) // Law of Cosines to find angle B angleB = acos((a² + c² - b²) / (2 * a * c)) // Law of Cosines to find angle C angleC = acos((a² + b² - c²) / (2 * a * b)) // Trigonometric functions sinA = sin(angleA) cosA = cos(angleA) tanA = tan(angleA)

Where:

a, b, c are the lengths of the sides of the triangle
angleA, angleB, angleC are the angles opposite sides a, b, and c respectively
sin, cos, tan are the sine, cosine, and tangent functions

Worked Example

Let's calculate the sine, cosine, and tangent values for a triangle with sides a=5, b=6, and c=7.

First, calculate angle A using the Law of Cosines:
angleA = acos((6² + 7² - 5²) / (2 * 6 * 7)) ≈ acos(0.848) ≈ 31.81°
Next, calculate angle B:
angleB = acos((5² + 7² - 6²) / (2 * 5 * 7)) ≈ acos(0.643) ≈ 49.44°
Then, calculate angle C:
angleC = acos((5² + 6² - 7²) / (2 * 5 * 6)) ≈ acos(-0.152) ≈ 98.75°
Now, calculate the trigonometric functions for angle A:
sinA ≈ sin(31.81°) ≈ 0.53 cosA ≈ cos(31.81°) ≈ 0.85 tanA ≈ tan(31.81°) ≈ 0.62

So for a triangle with sides 5, 6, and 7, the sine, cosine, and tangent values for the angle opposite side 5 are approximately 0.53, 0.85, and 0.62 respectively.

Frequently Asked Questions

Can I use this calculator for any type of triangle?

Yes, this calculator can be used for any triangle as long as you know the lengths of all three sides. The calculator will work for scalene, isosceles, and equilateral triangles.

What if the triangle is not valid?

The calculator will check if the given side lengths can form a valid triangle. If the sum of any two sides is less than or equal to the third side, the calculator will display an error message.

How accurate are the results?

The results are calculated using standard trigonometric functions and should be accurate to several decimal places. However, for practical purposes, you may want to round the results to a reasonable number of decimal places.