Step-by-Step: SOH CAH TOA
- Identify the angle you're working from and label the triangle's sides relative to it (opposite, adjacent, hypotenuse).
- Choose the right ratio based on which two sides you know or need.
- Solve algebraically for the missing value.
Worked Example
A ladder leans against a wall at a 60° angle, with its base 4 meters from the wall. How tall is the point where it touches the wall?
We know the angle and adjacent side, want the opposite side — that's Tangent.
tan(60°) = opposite / 4 → opposite = 4 × tan(60°) = 4 × 1.732 ≈ 6.93 meters
Frequently Asked Questions
Should my calculator be in degrees or radians?
For geometry problems like this one, use degrees. For calculus and physics, radians are almost always the expected unit — always check your calculator's mode first.
What if I know two sides but not the angle?
Use the inverse trig functions — arcsin, arccos, or arctan — to work backward from a ratio of two known sides to find the unknown angle itself.
