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**Disclaimer:**The results generated by the tool should be considered for educational purposes only. You are notified to consult an expert in case you consider calculations as a reference anywhere.

**Table of Content**

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

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 trigonometry 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.

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

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**

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°**