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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.

## 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
• 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.

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