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Solve Right Angle Is Without Sin Cos Tan Calculator

Reviewed by Calculator Editorial Team

This calculator solves right-angled triangles without using sine, cosine, or tangent functions. It uses the Pythagorean theorem and trigonometric identities to find all sides and angles when given two known values.

How to Use This Calculator

To solve a right-angled triangle without using sin, cos, or tan functions:

  1. Enter two known values from the triangle (two sides or one side and one angle).
  2. Select which values you've entered.
  3. Click "Calculate" to find the missing values.
  4. Review the results and chart visualization.

The calculator will determine the missing side(s) and angle(s) using the Pythagorean theorem and trigonometric identities.

Formulas Used

The calculator uses these fundamental trigonometric identities:

Pythagorean theorem: a² + b² = c² where c is the hypotenuse
Trigonometric identities: sin(θ) = opposite/hypotenuse cos(θ) = adjacent/hypotenuse tan(θ) = opposite/adjacent

These formulas are rearranged to solve for unknown values based on the given inputs.

Worked Examples

Example 1: Given two sides

If you know side a = 3 and side b = 4:

  1. Calculate hypotenuse c: √(3² + 4²) = 5
  2. Calculate angle opposite to side a: arcsin(3/5) ≈ 36.87°
  3. Calculate angle opposite to side b: arccos(4/5) ≈ 36.87°

Example 2: Given one side and one angle

If you know side a = 5 and angle A = 30°:

  1. Calculate side b: 5 * tan(30°) ≈ 2.887
  2. Calculate hypotenuse c: 5 / cos(30°) ≈ 5.774
  3. Angle B ≈ 60°

Note: Angles are calculated using the inverse trigonometric functions (arcsin, arccos, arctan) which are equivalent to sin⁻¹, cos⁻¹, and tan⁻¹ respectively.

Frequently Asked Questions

Can I solve a right-angled triangle without using sin, cos, or tan?
Yes, you can use the Pythagorean theorem and trigonometric identities to solve for all sides and angles when given two known values.
What if I only know one side and one angle?
The calculator will determine the other sides and angles using the given information and trigonometric identities.
Are the results accurate?
The calculator uses precise mathematical formulas and JavaScript's built-in trigonometric functions to ensure accurate results.
Can I use this calculator for non-right-angled triangles?
No, this calculator is specifically designed for right-angled triangles only.
What units should I use for the sides?
The calculator accepts any unit of length (cm, m, inches, etc.) as long as all inputs use the same unit.