Sohcahtoa Calculator

Sohcahtoa Calculator

Enter the sides or angles of the right triangle, and the calculator will find the missing sides and angles.

Leg (a)

Leg (b)

Height (c)

Area (α)

deg ▾

Area (β)

deg ▾

SOHCAHTOA Calculator

This SOHCAHTOA calculator helps you find missing sides or angles of right triangles using the SOH.CAH.TOA method, providing step-by-step solutions for easy learning.

What is SOHCAHTOA?

SOHCAHTOA is a mnemonic used to remember the formulas for the primary trigonometric ratios:

Sine (sin) = Opposite / Hypotenuse
Cosine (cos) = Adjacent / Hypotenuse
Tangent (tan) = Opposite / Adjacent

Right Triangle Illustration

Definitions:

Hypotenuse: The longest side, opposite the right angle
Opposite side: The side opposite the acute angle of interest
Adjacent side: The side next to the acute angle, but not the hypotenuse

How SOHCAHTOA Helps

SOHCAHTOA tells you which trigonometric ratio to use to find unknown sides or angles:

SOH: sin(θ) = Opposite / Hypotenuse
CAH: cos(θ) = Adjacent / Hypotenuse
TOA: tan(θ) = Opposite / Adjacent

Memorizing SOHCAHTOA

Use simple mnemonic phrases to remember the ratios, e.g., “Oscar Had A Heap Of Apples”:

Sin(θ) = Oscar / Had = Opposite ÷ Hypotenuse
Cos(θ) = A / Heap = Adjacent ÷ Hypotenuse
Tan(θ) = Of / Apples = Opposite ÷ Adjacent

How to Solve Missing Sides Using SOHCAHTOA

Identify the known and unknown sides of the triangle.
Select the appropriate trig ratio (sin, cos, or tan).
Substitute the known values into the formula.
Solve for the unknown side or angle using algebra.

Example

Find the length of the side opposite a 30° angle in a right triangle with a hypotenuse of 13 cm.

Solution:

We are looking for the opposite side (use SOH formula):

sin(30°) = Opposite / 13

sin(30°) = 0.5

0.5 = Opposite / 13 → Opposite = 0.5 × 13 = 6.5 cm

Save time with our SOHCAHTOA calculator, which automatically finds missing sides and angles using these formulas.

Does SOHCAHTOA Only Work for Right Triangles?

Yes. These relationships rely on a right angle being present. For non-right triangles, the standard definitions of opposite, adjacent, and hypotenuse do not apply.

SOHCAHTOA Measures for Common Angles

SOHCAHTOA Measures of Popular Angles