How to Calculate Sohcahtoa in Spreadsheets

The Trigonometry of Right Angled Triangles in Excel and Calc

Nov 25, 2008

Sohcahtoa and Spreadsheets, Mark Alexander Bain

Sohcahtoa has been used by generations of teachers with generations of school children; it can now be made much easier by using spreadsheets.

When it comes to trigonometry one of the most useful shapes is the right angled triangle - especially when used with that age old acronym sohcahtoa; and a spreadsheet's formulae can help bring everything together.

What Does Sohcahtoa Mean?

Sohcahtoa is a simple acronym passed on by many a teacher to help school children remember the trigonometric relationships built into any right angled triangle:

soh stands for sine = opposite over hypotenuse
cah stands for cosine = adjacent over hypotenuse
toa stands for tangent = opposite over adjacent

Spreadsheets and Trigonometric Functions

It is important to note that Spreadsheets such as Excel and Calc use radians, and not degrees, when calculating trigonometric functions; therefore:

=ASIN(0.5)

will not return 30 degrees (as every schoolchild would expect), it actually returns 0.52 radians, and so this must be converted from radians to degrees:

=DEGREES(ASIN(0.5))

So, to calculate the Sine of a an angle in degrees it must first be converted to radians:

=SIN(RADIANS(30))

The result from this would, of course, then be 0.5.

Trigonometry, Right Angled Triangles, Spreadsheets and Sines

The starting point is to input the length of the sides of the right angled triangle so that:

A1 = length of hypotenuse
B1 = length of side adjacent to angle
C1 = length of side opposite the angle

Now from the soh from sohcahtoa the following is deduced:

sine = opposite / hypotenuse

And then that can be turned into a spreadsheet formula:

=C1/A1

Trigonometry, Right Angled Triangles, Spreadsheets and Cosines

Just like Sines Cosines can be found sohcahtoa:

cosine = adjacent / hypotenuse

And again, this can be turned into a formula:

=B1/A1

Trigonometry, Right Angled Triangles, Spreadsheets and Tangents

The final step is to take the toa from sohcahtoa:

tangent = opposite / adjacent

And produce another (but very similar) formula:

=C1/B1

A Simple Example

In this simple example one of the inside angles of a 3-4-5 right angled triangle is calcualted:

A1: 5

B1: 4

C1: 3

D1: =B1/A1

E1: =DEGREES(ASIN(D1))

The end result is 53.13 degrees.

Summary

The trigonometric relationships from a right angled triangle can easily be worked out by using the acronym sohcahtoa; and sohcahtoa can be broken down into:

soh stands for sine = opposite over hypotenuse
cah stands for cosine = adjacent over hypotenuse
toa stands for tangent = opposite over adjacent

If the lengths of the side of a right angled triangle are entered into a spreadsheet (such as Microsoft Excel or OpenOffice.org Calc) so that:

A1 = length of hypotenuse
B1 = length of side adjacent to angle
C1 = length of side opposite the angle

Then the trigonometric functions can be found from:

Sine: =C1/A1
Cosine: =B1/A1
Tangent: =C1/B1

It must also be remembered that spreadsheets work in radians and not degrees.

The copyright of the article How to Calculate Sohcahtoa in Spreadsheets in Computer Programming is owned by Mark Alexander Bain. Permission to republish How to Calculate Sohcahtoa in Spreadsheets in print or online must be granted by the author in writing.

Sohcahtoa and Spreadsheets

Trigonometry and the Right Angled Triangle

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