# Soh Cah Toa help

• Jul 6th 2005, 04:00 PM
mattballer082
Soh Cah Toa help
in geometry, is anyone familiar with SOH CAH TOA?

First, what is the definition of adjacent and how do i know which angle is adjacent and which angle is opposite. I know which is the hypotenuse.
How would I use it with SINE COSINE and TANGENT??

• Jul 6th 2005, 07:47 PM
Math Help
In short, opposite is the side opposite any angle you are taking the sin, cos or tan of. Adjacent is the side that is part of(or next to) the angle but not the hypotenuse.

Remember that Soh Cah Toa always refers to right triangles (triangles with at least one 90 degree angle).

The hypotenuse is always the side opposite the 90 degree angle.

in fact the hypotenuse is the opposite for the 90 degree angle, take a look:

$\displaystyle sin=\frac{opposite}{hypotenuse}$

$\displaystyle sin(90)=1$

$\displaystyle 1=\frac{opposite}{hypotenuse}$

therefore

$\displaystyle opposite=hypotenuse$

And that is why sin(90) = 1, because the hypotenuse is opposite the right angle.

I hope I didn't confuse you too much.;)
• Jul 6th 2005, 11:14 PM
ticbol
I am not familiar with SOH CAH TOA (they were not taught to us in school back then), but I have encountered those more than once, so I can explain them.

SOH
S = O/H
Sine = Opposite / Hypotenuse

CAH
C = A/H

TOA
T = O/A

SOH CAH TOA then is a way to memorize or recall which one, or what is sine, cosine or tangent.

Of course you know that sine, cosine and tangent are trigonometric functions of an angle.
This angle is imagined as one of the two acute angles of a right triangle.

A right triangle has a hypotenuse, which is the longest of the 3 sides, and two other sides that are perpendicular to each other. These other two perpendicular sides are sometimes called "legs" of the right triangle.

The angle in question is opposite to one of these two legs. The angle then is adjacent to the other leg.
The leg opposite to the angle is the "Opposite"