Question

Write an explanation of SOHCAHTOA as if you are explaining what it represents to a new geometry student. Include at least one diagram. Be thorough.

Answer 1

SOHCAHTOA means

`\begin{gathered} SOH\sin \theta=\frac{opposite}{\text{hypotenuse}} \\ CAH\cos \theta=\frac{adjacent}{\text{hypotenuse}} \\ TOA\tan \theta=\frac{opposite}{\text{adjacen}} \\ \theta\text{ is an acute angle, that is an angle less than 90}\degree \end{gathered}`

A right-angle triangle is a triangle that has one of its interior angle as 90 degrees. So the other two angles in a right-angle triangle are acute (they are less than 90 degrees)

A right angle triangle has three sides which are

hypotenuse h : which is the longest side or the side facing angle 90 degrees

opposite o : which is the side facing the acute angle

adjacent a : which is the side that contains the acute angle and the 90 degrees angle.

See diagram below