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Sohcahtoa Calculator

Enter any two given values into the SOHCAHTOA calculator to find a missing sides and an angle of the right triangle.

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SOHCAHTOA Calculator

This calculator uses the SOH.CAH.TOA mnemonic method to solve the sides and angles of a right triangle. It provides step-by-step calculations using the SOHCAHTOA formula, which we are going to mention below.

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). Here's what each letter in the acronym stands for:

  • S: Sine
  • O: Opposite Side
  • H: Hypotenuse 
  • C: Cosine
  • A: Adjacent side
  • T: Tangent

It refers to which of the trig ratios can be used for finding missing sides and angles based on the formulas below. 

SOH: (Sin (θ)) = Opposite Hypotenuse

CAH: (Cos (θ)) = Adjacent Hypotenuse

TOA: (Tan (θ)) = Opposite Adjacent

Even the sohcahtoa calculator implements these formulas to calculate missing sides and angles. 

SOHCAHTOA

In the Diagram:

  • 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

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 

How to Solve Missing Sides Using SOHCAHTOA?

There are steps to work out the unknown sides of a right-angled triangle:

  • List out the sides of the right-angled triangle 
  • Select the trig ratio that is about the information we should have
  • Put the values into the trigonometric function and find the missing side 

Example:

We have a right triangle with a following measurement:

  • Hypotenuse = 13 cm
  • Angle α = 30 °

Find the missing side that is opposite to the acute angle. 

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. 

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 

SOHCAHTOA Measures of Popular Angles:

  $$ {\displaystyle \sin \theta } $$ $$ {\displaystyle \cos \theta } $$ $$ {\displaystyle \tan \theta =\sin \theta {\Big /}\cos \theta } $$
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 $$ {\displaystyle {\frac {\sqrt {\mathbf {\color {red}{4}} }}{2}}=\;\,1} $$ $$ {\displaystyle {\frac {\sqrt {\mathbf {\color {blue}{0}} }}{2}}=\;\,0} $$ $$ {1{\Big /}0\;\;= \text {Undefined}} $$