What is the SOHCAHTOA Calculator?
SOHCAHTOA is the classic mnemonic for the three primary trigonometric ratios in a right triangle: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, and Tan = Opposite/Adjacent. This calculator uses those ratios to solve a right triangle when you know the acute angle \(\theta\) and exactly one side length.
How to use it
Enter the angle \(\theta\) in degrees (between 0 and 90), then type a value into exactly ONE of the three side fields — Opposite, Adjacent, or Hypotenuse. Leave the other two blank (or 0). The calculator detects the known side and computes the remaining two, plus the sine, cosine, and tangent of \(\theta\).
The formulas explained
For a right triangle, the angle \(\theta\) relates the sides as:
$$\sin\theta = \dfrac{\text{Opposite}}{\text{Hypotenuse}}, \quad \cos\theta = \dfrac{\text{Adjacent}}{\text{Hypotenuse}}, \quad \tan\theta = \dfrac{\text{Opposite}}{\text{Adjacent}}$$Rearranging lets you solve for any missing side. For example, if you know the opposite side:
$$\text{Hypotenuse} = \frac{\text{Opposite}}{\sin\theta} \qquad \text{Adjacent} = \frac{\text{Opposite}}{\tan\theta}$$
Worked example
Suppose \(\theta = 45°\) and the opposite side = 5. Then \(\sin 45° \approx 0.7071\) and \(\tan 45° = 1\). So
$$\text{Hypotenuse} = 5 \div 0.7071 \approx 7.0711 \qquad \text{Adjacent} = 5 \div 1 = 5$$The triangle therefore has opposite 5, adjacent 5, and hypotenuse \(\approx 7.0711\) — an isosceles right triangle, as expected for 45°.
FAQ
Which side should I enter? Just one. If you fill in more than one, the calculator uses the first non-empty in the order Opposite, Adjacent, Hypotenuse.
Does it work in radians? No — enter the angle in degrees; it is converted internally.
What if \(\theta\) is 0 or 90? Some ratios become 0 or undefined (division by zero), so those edge angles return 0 for the affected side. Use an angle strictly between 0° and 90° for a valid triangle.
