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subject: Tangent Ratios [print this page]

Learning sohcahtoa with examples:
Learning sohcahtoa with examples:

The word sohcahtoa plays an important role in the major part of trigonometry. This term is very much oriented with right triangle and trigonometric ratio. Actually that is not a word. We could say that sohcahtoa is an abbreviation. let us expand it.

s- sine

o- opposite side

h- hypotenuse

c - cos

a- adjacent side

t - tangent

The term sohcattoa helps to remember the formula of trigonometric ratio sine, cosine and tangent.

Expanation on Sohcahtoa with Examples:

sohcahtoa

Sine of any angle is defined as the ratio of the side opposite to the angle to the side which is opposite to 90 degrees.

Cosine of any angle is defined as the ratio of the side adjacent to the angle to the side which is opposite to 90 degrees.

Tangent of any angle is defined as the ratio of the side opposite to the angle to the side adjacent to the angle.

Note: The side opposite to 90 degrees is called as hypotenuse.

Hypotenuse = 'sqrt(x^2 + y^2)'

where x and y are the opposite and adjacent sides.

Helping to do Examples with Sohcahtoa:

Given that tan B = 3/4. Find the opposite side, adjacent side and hypotenuse.

Solution:

tan B = 3/4 i.e., opposite side/adjacent side.

So, opposite side = 3

adjacent side = 4

hypotenuse = 'sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5'

For the given figure, using the term sohcahtoa find sin p. cos p and tan p.

sin p = opposite side/ hypotenuse = 32/40

To find cos p we need adjacent side.

sohcahtoa examples

adjacent side =

= sqrt(576)

= 24

cos p = 24/40

tan p = 32/40

If sin A = 12/13, find the value of cos A, tan A.

Solution:

sin A = 12 / 13

We know the abbreviation of sohcahtoa.

So, the opposite side is 12 and hypotenuse is 13. Let us find the adjacent side.

adjacent side = 'sqrt(13^2 - 12^2) = sqrt (25) = 5'

So, cos A = 5/13

tan A = 12/5

The tangent ratio can be used to calculate the length of one of the shorter sides (legs) of a right triangle. To do this you need the tangent ratio for one of the smaller angles, and the length of one leg of the triangle.

There are two types of these problems, depending on whether you are finding the opposite or adjacent side.

Press the F5 key to display the parameters box:

You enter the given information into these edit boxes as follows:

edit box 'A' = given angle less than 90.

NOTE: Just type a number for the angle A. Do NOT use the degree operator: after the angle.

edit box 'B' = adjacent side to A.

edit box 'C' = opposite side to A.

Set one only of B or C to a non-zero value.

Set the unknown value to zero.

NOTE: In the diagram of the parameters box above, A=35, B=10, and C=0. This means we are solving the same problem as example 1 above. We are given an angle of 35, and the adjacent side to this angle of length 10. We are calculating the length of the opposite side.

Click the 'Update' button to refresh the diagram and calculations.

Step 3 Adjust the size of the diagram

If the triangle diagram is too big to display properly on your computer screen, briefly press the F10 key to reduce its size. To make the diagram bigger, hold down a Ctrl key while you press F10.

by: johnharmer

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