Sohcahtoa Calculator

Enter two known values of a right triangle, such as two sides or one side and one angle, to calculate the missing side lengths or angles.

Note: Enter two sides, or one side and one angle.

Leg (a)

Leg (b)

Hypotenuse (c)

Angle (α)

deg ▾

Angle (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.

What is SOHCAHTOA?

SOH CAH TOA is a mnemonic way used to remember the formulas for main trigonometric ratios including sine (sin), cosine (cos), and tangent (tan).

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

Right Triangle Illustration

Definitions:

Here is what the terms mean:

Hypotenuse: The longest side, always opposite to the right angle
Opposite side: The side directly opposite to an acute angle
Adjacent side: The side that is connected to an acute angle and opposite

SOHCAHTOA Formula Explained:

Sine Formula (SOH):

Formula:

sin(θ) = Opposite Hypotenuse

Explanation:

👉 Use the sine ratio to find unknown side lengths or angles when the opposite side and hypotenuse of a right triangle are known.

Cosine Formula (CAH):

Formula:

cos(θ) = Adjacent Hypotenuse

Explanation:

👉 Use the cosine ratio when working with the adjacent side and the hypotenuse. This is useful for finding unknown sides or angles in right triangles.

Tangent Formula (TOA):

Formula:

tan(θ) = Opposite Adjacent

Example:

tan(35°) = sin(35°) ÷ cos(35°) ≈ 0.7002

Explanation:

👉 You must use the tangent ratio when you know the opposite and adjacent sides of a right triangle. It is especially useful when the hypotenuse is not involved.

How to Use the SOHCAHTOA Calculator?

Follow these steps to use our SOHCAHTOA calculator accurately:

Enter two known values of the right triangle, such as two sides or one side and one angle
Click the "Calculate" button to solve the right triangle
View the results, including the missing side lengths or angles and the step-by-step calculations

When to Use SOHCAHTOA?

You can use SOHCAHTOA whenever you are working with a right triangle and know one acute angle and at least one side.

Here are some common real-world applications:

Measure distances that are difficult or impossible to measure directly
Calculate the height of buildings, trees, towers, and other tall structures
Solve physics problems involving forces, vectors, and projectile motion
Perform calculations in civil, structural, and mechanical engineering
Design roofs, staircases, ramps, and other construction projects
Conduct land surveying and topographic mapping
Assist with architectural planning and structural design
Find missing sides or angles in right triangles
Solve trigonometry problems in school, college, and competitive exams

How To Solve Missing Sides Using SOHCAHTOA?

Follow these steps to work out the unknown sides of a right-angled triangle:

Write down the known and unknown sides of the right-angled triangle
Select the trig ratio that can be used to find the unknown values
Put the values into the chosen trigonometric ratio and isolate the unknown side
Perform the necessary calculations according to the chosen trig ratio and get the unknown values

Example:

A right triangle has a hypotenuse of 13 cm and an acute angle (α) of 30°. Determine the length of the side opposite angle α

Solution:

Solution:

We are looking for the opposite side by having the hypotenuse, so use the SOH formula. Hence put the values and get to know the missing side.

Sin (30°) = Opposite 13 cm

We also know that Sin (30°) is a fixed value (0.5)

0.5 = Opposite 13 cm

Now, to find the missing opposite side, we can multiply both sides of the equation by 13 cm.

Opposite = 0.5 * 13 cm

Opposite = 6.5 cm

To save time and effort, try our trigonometry SOHCAHTOA calculator. It uses the SOHCAHTOA formulas to calculate the missing sides/angles of the right triangles.

How To Easily Remember SOHCAHTOA?

It is easy to remember the sequence of Sin, Cos, and Tan. You need to try memorable phrases such as:

“Oscar Had A Heap Of Apples”:

It implies to right angle trig functions as:

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

Does Soh Cah Toa Only Work on Right Triangles?

Yes, it only works in the cases of right triangles. In non-right triangles, the side relationships(Hytoneous, Opposite, and Adjacent) do not hold. Therefore, it's not possible to apply SOCAHTOA to them.

Common SOHCAHTOA Mistakes:

Most of the students get wrong answer not because the formula is difficult, they apply the wrong side or angle in the formula:

1. Mixing Up Opposite and Adjacent:

Wrong: Choosing the side next to the angle as “opposite.”

Correct:

Opposite = side directly across from the chosen angle
Adjacent = side next to the chosen angle (but not the hypotenuse)

👉 Tip:

First of all, identify the angle first, and after that label the sides.

2. Using the Wrong Angle:

Wrong: Using the other acute angle in the triangle.

Correct: SOHCAHTOA is always based on the specific angle given in the problem.

Remember:

The “opposite” and “adjacent” sides change when the angle changes.

3. Confusing the Hypotenuse:

Wrong: Considering any long side as the hypotenuse.

Correct: The hypotenuse is always:

The side opposite the right angle
The longest side of the triangle

👉 Quick Check:

Find the 90° angle first and then the side across from it is the hypotenuse.

If you are unsure which side is the hypotenuse or need to calculate its length, try our Pythagorean Theorem Calculator before applying SOHCAHTOA.

Final Tip:

Before calculating:

Identify the right angle and mark it
Select the given angle
Label Opposite, Adjacent, and Hypotenuse.
Then apply SOH, CAH, or TOA.

By keeping these points in mind, you can avoid the most common SOHCAHTOA mistakes and solve trigonometry problems more accurately.

SOHCAHTOA Measures of Popular Angles:

SOHCAHTOA Measures of Popular Angles

Sohcahtoa Calculator

SOHCAHTOA Calculator:

What is SOHCAHTOA?

Definitions:

SOHCAHTOA Formula Explained:

Sine Formula (SOH):

Cosine Formula (CAH):

Tangent Formula (TOA):

How to Use the SOHCAHTOA Calculator?

When to Use SOHCAHTOA?

How To Solve Missing Sides Using SOHCAHTOA?

Example:

How To Easily Remember SOHCAHTOA?

Does Soh Cah Toa Only Work on Right Triangles?

Common SOHCAHTOA Mistakes:

1. Mixing Up Opposite and Adjacent:

2. Using the Wrong Angle:

3. Confusing the Hypotenuse:

Final Tip:

SOHCAHTOA Measures of Popular Angles:

References: