SohCahToa Definition

SohCahToa Definition

SohCahToa: SOHCAHTOA is a mnemonic device that is worn in mathematics to remember the definitions of the three most common trigonometric functions. This lesson will reveal each one and give patterns, and you’ll have the moment to take a quiz at the end to strengthen what you’ve learned.

SOHCAHTOA. A way of remembering how to compute the sine, cosine, and tangent of an angle. SOH stands for Sine equivalents Opposite over Hypotenuse. CAH lasts for Cosine equals Adjacent over Hypotenuse. TOA stands for Tangent compares Opposite over Adjacent.

 SohCahToa Definition

 Soh Cah Toa Calculator

Sine, cosine, and contiguous are the three main functions in trigonometry. They’re all based on ratios obtained from a right triangle. Before we can discuss what ratios work for which function, we need to label a right triangle.

The ratios that allow you to demonstrate the sine, cosine, and tangent of a right triangle are:Opposite is the side opposite the angle in uncertaintyadjacent is the side next to the angle in investigation, and the hypotenuse is the longest side of a right sure. The hypotenuse is always opposite the right angle.

  • The sine of an angle is equal to the side opposite the angle divided by the hypotenuse.
  • The cosine of an angle is comparable to the side adjacent to the angle divided by the hypotenuse.
  • The tangent of an comparable is equal to the side opposite the angle divided by the side adjacent to the angle.

These proportion can be difficult to remember. You might easily get confused and not remember which side goes where. SOHCAHTOA is a mnemonic device helpful for commemorating what ratio goes with which business.

  • SOH = Sine is Opposite over Hypotenuse
  • CAH = Cosine is Adjacent over Hypotenuse
  • TOA = Tangent is Opposite over Adjacent

With these properties, you can solve almost any problem related to finding either a side length or point of view measure of a right triangle. SohCahToa can ensure that you won’t get them wrong.

Soh Cah Toa Problems

A way of remembering how to compute the sine, cosine, and tangent of an angle.

SOH stands for Sine equals contradictory over Hypotenuse.

CAH stands for Cosine equals Adjacent over Hypotenuse.

TOA stands for Tangent equals Opposite over Adjacent.

Example: Find the values of sin θ, cos θ, and tan θ in the right triangle shown.
Answer: sin θ = 3/5 = 0.6

cosθ = 4/5 = 0.8

tanθ = 3/4 = 0.75

This triangle is oriented separately than the one shown in the SOHCAHTOA diagram, so make sure you know which sides are the opposite, adjacent, and hypotenuse.

Trigonometry Soh Cah Toa

let’s see what this is all about.

Firstly, the names Antithesis, Adjacent and Hypotenuse come from the right triangle:

triangle showing Opposite, Adjacent and Hypotenuse

  • “Opposite” is antithetical to the angle θ
  • “Adjacent” is adjacent (next to) to the angle θ
  • “Hypotenuse” is the long one

examples of Opposite, Adjacent and Hypotenuse

Adjacent is always next to the angle

And Opposite is opposite the angle

Sine, Cosine and Tangent

And SineCosine and Tangent are the three main gatherings in trigonometry.

They are often shortened to sincos and tan.

The calculation is simply one side of a right angled triangle divided by another side … we just have to know which sides, and that is where “sohcahtoa” helps.

For a triangle with an angle θ , the functions are calculated this way:

sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent


Example: what are the sine, cosine and tangent of 30° ?

A 30° triangle has a hypotenuse (the long side) of length 2, an opposite side of length 1 and an adjacent side of √3, like this:

Now we know the lengths, we can calculate the functions:

sin(30°) = 12 = 0.5
cos(30°) = 1.732…2 = 0.866…
tan(30°) = 11.732… = 0.577…

(get your calculator out and check them!)

A way to remember the definitions of the three most common trigonometry functions: sin, cos and tan.

Used as a memory aid for the definitions of the three common trigonometry functions sine, cosine and tangent. When spoken it is usually pronounced a bit like “soaka towa”.

SOH Sine = Opposite over Hypotenuse.
CAH Cosine = Adjacent over Hypotenuse.
TOA Tangent = Opposite over Adjacent.

Soh Cah Toa Formula

Now, for some example problems. Let’s find x for this triangle.

Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent

tan 60 = x/13We know the side adjacent to the known angle of 60 degrees is 13 cm. We’re trying to find the length of the side opposite the known angle of 60 degrees. Thus, we need to use TOA, or tangent (tan), which uses opposite and adjacent. Therefore, our equation will be:

The tan of 60 is 1.73, which makes the equation:

1.73 = x/13

Solve for x to get:

x = (1.73) * (13) = 22.49

So, the length of side x is 22.49 cm.

On to another example problem. What is the sine of 35 degrees?

sin 35 = 2.8 / 4.9 = 0.57The sine of an angle is equal to the opposite side divided by the hypotenuse.

And for one final problem, find sin, cos and tan for the angle in the right triangle shown.

cos = adjacent/hypotenuse = 4 / 5 = 0.8sin = opposite/hypotenuse = 3 / 5 = 0.6

tan = opposite/adjacent = 3 / 4 = 0.75

Real-Life ExamplesTrigonometric functions are important for many reasons. They let you calculate angles when you know sides and calculate sides when you know angles. This can be helpful in many real life situations, such as when determining the height of a large building or the distance across a lake – things that just can’t be measured easily.

How do you remember Sin Cos values?

Divide your sine values by the cosine values to fill the tangent column. Simply speaking, tangent = sine/cosine. Thus, for every angle, take its sine value and divide it by its cosine value to calculate the corresponding tangent value. To take 30° as an example: tan 30° = sin 30° / cos 30° = (√1/2) / (√3/2) = 1/√3.

What does SOH CAH TOA mean in texting?

DefinitionSOHCAHTOA. Sine (Opposite over Hypotenuse), Cosine (Adjacent over Hypotenuse), Tangent (Opposite over Adjacent) SOHCAHTOA. Sex on Hard Concrete Always Hurts Try Other Alternatives (mnemonic for remembering sine, cosine and tangent)

How do you work out Soh?

In any right angled triangle, for any angle:
  1. The sine of the angle = the length of the opposite side. the length of the hypotenuse.
  2. The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.
  3. The tangent of the angle = the length of the opposite side. the length of the adjacent side.