SOH CAH TOA Calculator
The ultimate right-triangle solver. Calculate precise trigonometric ratios from known angle degrees, or work backwards using inverse functions (arcsin, arccos, arctan) to find missing angles from 2 known side lengths.
Find ratio from Angle
Find Angle from sides
2. Enter Values
How Trigonometry Ratios Work
SOH CAH TOA is the most famous acronym in mathematics for a reason. It perfectly summarizes the three core trigonometric ratios that define all right-angled triangles. If you know an angle, these ratios tell you exactly how the side lengths must scale relative to each other.
SOH
Sine compares the side directly across from the angle (Opposite) to the longest outer wall of the triangle (Hypotenuse).
CAH
Cosine compares the side touching the angle (Adjacent) to the longest outer wall of the triangle (Hypotenuse).
TOA
Tangent is completely independent of the Hypotenuse. It only compares the Opposite wall directly against the floor wall (Adjacent).
Finding the Missing Angle (Inverse Trig)
Oftentimes, you are handed a physical triangle where you can measure two of the border walls with a ruler, but you don't have a protractor to measure the inner corner angles. This is where Inverse Trigonometry (arcsin, arccos, arctan) shines.
Example: Using Arctangent (Tan⁻¹)
- Problem: You measured the Opposite side as 5cm, and exactly Adjacent to your corner is a side measuring 8cm. What is the angle?
- Step 1: Choose the right SOH CAH TOA formula. Since you have Opposite and Adjacent, you must use TOA.
- Step 2: Build the ratio (Opposite / Adjacent): 5 / 8 = 0.625
- Step 3: Feed the ratio into the Inverse formula: 𝘛𝘢𝘯⁻¹(0.625)
- Result: The angle is exactly 32.0054°
Frequently Asked Questions
Struggling with Trig Homework?
Share this SOH CAH TOA calculator with your study group or classmates to instantly verify complex inverse trigonometry angles before handing in a test.
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