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Math Calculators ▶ Sohcahtoa Calculator

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**Table of Content**

The SOHCAHTOA calculator follows this particular mnemonics to resolve for trigonometric functions of a right-angled triangle.

In this technical read below, we will help you in understanding the actual meaning of SOHCAHTOA and how it can be handy in resolving various trig angles and sides.

In Trigonometry, SOHCAHTOA is defined as follows:

**SOH (Sin(θ))= Perpendicular/Hypotenuse**

**CAH (Cos(θ)) = Base/Hypotenuse**

**TOA (Tan(θ))= Perpendicular/Base**

Our SOHCAHTOA solver also considers the same correlated formulas so as to depict triangle sides and angles measurements.

Most of us still find it tricky and confusing to remember trig ratios. No doubt only three sides and angles are there to deal with. But the probability of exact recalling every time is still faded for us. Keeping in view this issue, we have developed this SOH CAH TOA calculator to assist you people in identifying the right trigonometry ratio.

Putting things simple now, let’s have a look at the following triangle below:

In this triangle, three sides are labelled as:

The side that is opposite to acute angle

The side that is connected to acute angle and opposite

The longest side of Right Angle triangle whose one end is connected to base, while other is connected to opposite

The SOHCAHTOA calculator assists you to determine all these ratios in a matter of seconds, thereby reducing your lengthy calculations’ time.

Let us code here that we have also designed another pythagorean theorem calculator that introduces a lot of ease while you are about to determine only triangle sides.

Trigonometry runs around some basic angle measurements that form the basis of angle and side calculations under the subject. These are given as follows:

$$ {\displaystyle \sin \theta } $$ | $$ {\displaystyle \cos \theta } $$ | $$ {\displaystyle \tan \theta =\sin \theta {\Big /}\cos \theta } $$ | |

0° = 0 radians | $$ {\displaystyle {\frac {\sqrt {\mathbf {\color {blue}{0}} }}{2}}=\;\;0} $$ | $$ {\displaystyle {\frac {\sqrt {\mathbf {\color {red}{4}} }}{2}}=\;\;1} $$ | $$ {\displaystyle \;\;0\;\;{\Big /}\;\;1\;\;=\;\;0} $$ |

30° = π/6 radians | $$ {\displaystyle {\frac {\sqrt {\mathbf {\color {teal}{1}} }}{2}}=\;\,{\frac {1}{2}}} $$ | $$ {\displaystyle {\frac {\sqrt {\mathbf {\color {orange}{3}} }}{2}}} $$ | $$ {\displaystyle \;\,{\frac {1}{2}}\;{\Big /}{\frac {\sqrt {3}}{2}}={\frac {1}{\sqrt {3}}}} $$ |

45° = π/4 radians | $$ {\displaystyle {\frac {\sqrt {\mathbf {\color {green}{2}} }}{2}}={\frac {1}{\sqrt {2}}}} $$ | $$ {\displaystyle {\frac {\sqrt {\mathbf {\color {green}{2}} }}{2}}={\frac {1}{\sqrt {2}}}} $$ | $$ {\displaystyle {\frac {1}{\sqrt {2}}}{\Big /}{\frac {1}{\sqrt {2}}}=\;\;1} $$ |

60° = π/3 radians | $${\displaystyle {\frac {\sqrt {\mathbf {\color {orange}{3}} }}{2}}} $$ | $$ {\displaystyle {\frac {\sqrt {\mathbf {\color {teal}{1}} }}{2}}=\;{\frac {1}{2}}} $$ | $$ {\displaystyle {\frac {\sqrt {3}}{2}}{\Big /}\;{\frac {1}{2}}\;\,={\sqrt {3}}} $$ |

90° = π/2 radians | $$ {\displaystyle {\frac {\sqrt {\mathbf {\color {red}{4}} }}{2}}=\;\,1} $$ | $$ {\displaystyle {\frac {\sqrt {\mathbf {\color {blue}{0}} }}{2}}=\;\,0} $$ | $$ {\displaystyle \;\;1\;\;{\Big /}\;\;0\;\;=}
Undefined $$ |

Following are the most broadly implemented SOHCAHTOA ratios in calculus and analytic geometry:

**Sine = Perpendicular/Hypotenuse**

**Cosine = Base/Hypotenuse**

**Tangent = Perpendicular/Base**

**Secant = Hypotenuse/Perpendicular**

**Cosecant = Hypotenuse/Base**

**Cotangent = Base/Perpendicular**

**Arcsin = sin^{-1}x**

**Arccos = cos^{-1}x**

**Arctan = tan^{-1}x**

**Arcsec = sec^{-1}x**

**Arccosecant = cosec^{-1}x**

**Arccotangent = cot^{-1}x**

Another most widely used sentence that help you recalling the trig functions as follows:

**“Oscar Had A Heap Of Apples”**

Which implies that:

**Sin(θ) = Oscar / Had****Cos(θ) = A / Heap****Tan(θ) = Of / Apples**

Let us resolve an example that will help you to apply SOHCAHTOA to find side and angle of a right angled triangle!

For the triangle given as under, apply SOH CAH TOA find angle and side r:

**Solution:**

Here we have:

**sin(20°) = 10/r**

**r{sin(20°)} = 10**

**r = 10/sin(20°)**

**r = 10/0.3420**

**r = 29.239**

Now you must be thinking how to find angles using SOHCAHTOA. Let us guide you!

**Angle 1 = 90°**

**Angle 2 = 20°**

**Angle 3 = ?**

So we have:

**Angle 3 = 90° – 20°**

**Angle 3 = 70°**

Following is the input guide that will help you to know how to use this SOHCAHTOA triangle calculator:

**Input:**

- Among 6 input fields, enter only two in their respective fields
- After that, simply tap the calculate button

**Output:**

The free SOH CAH TOA calculator employs SOHCAHTOA to find angles and sides of the triangle ratios entered

Yes, definitely! SOHCAHTOA is only applicable to right triangles. In case you have acute, obtuse, or oblique triangles, you are supposed to get nothing from this technique.

You can also use the technique when you are given certain triangle sides and are asked to determine the rest of the sides and angles of the triangle.

SOHCAHTOA makes it possible to simplify calculations for trig values of a right angled triangle. and to fasten the results with 100% accuracy, pupils and professionals rely on our best SOHCAHTOA calculator.

From the source of Wikipedia: Hexagon chart