# Algebra 1 help....Tangent of an angle?

The tangent of an angle is equal to the ratio of the

adjacent side over the opposite side

hypotenuse over the opposite side

opposite side over the adjacent side

Relevance

SOH CAH TOA

• It is the opposite side divided by the adjacent side:

Good to way to set it in your mind is get you a piece of graphing paper. Or a piece of notebook paper will work since we are not being accurate we are just drawing it out to have a visual picture in out minds:

One: black felt tip pen!

One: Red felt tip pen! (or other color pen)

With the black felt tip pen:

In the center of the paper going across the paper drawn you a straight line:

With the black felt tip pen:

In the center of the paper gong up and down the page draw you another straighter line:

Label the line going across the page X:

Label the line going up and down the page Y:

Where the two line meet and cross is called your X, Y axis! Now don't get confused because a lot of teachers also refer to this as your X, Y intercept instead of axis: :

Now switch to your red (or other color) felt tip pen for drawing the triangle:

Where the two lines cross each other (X, Y axis or intercept) draw you a line out along the X line. This is the base of your triangle. or adjacent side:

Make it oh! approximately half way between the X, Y (axis or intercept) and the end of the page:

Now at the end of that line draw you a line going up at a right angle approximately half way up the page. This is your height of the triangle or opposite side:

Now label the bottom of the triangle as either the base, or adjacent side of the triangle

Now label the line going up at a right angle from your base as either the height, or opposite side of the triangle

Label line angling up from the X, Y (axis or intercept) to the top of the opposite side line as the hypotenuse of the triangle.

Note: the hypotenuse is aso called the slope line or slope!

Note: the angle Theta is the the angle formed where the hypotenuse and the base (adjacent side) meet: (intercepts) this is the angle you are looking for: the tangent of:

tangent (of theta) = height divided by base height / base

tangent (of Theta) = opposite side divided by adjacent side

Once you find the tangent you use the <tan^-1> function on your calculator or the chart in you book to find the angle of Theta. (angle formed where the base of the triangle and the hypotenuse meet (intercept) at the X, Y axis.

Some commonly used ways to label the sides of a right triangle:

A, B, C triangle were

B = opposite side

C = hypotneuse

X, Y, Z triangle were

Y = opposite side

Z = hypotenuse

Rise to Run (construction trades) like in roofs on buildings

Rise = the opposite side

Slope = hypotneuse

• Anonymous

remember SOHCAHTOA.

remember it like this:

Some old horse, caught a horse, taking oats away.

• remember soh cah toa. This means that the sine = opposite/hypotenuse, cosine= adjacent/hypotenuse, and tangent= opposite/adjacent.

• opposite side over the adjacent side

• opposite side over the adjacent side

• This is what I was taught...remember, "Some Old Hippie Caught Another Hippie Trippin' On Acid."

You'll Notice the first letters are SOHCAHTOA

S=O/H

C=A/H

T=O/A

Where S=Sine, O=Oppositie, H=Hypotenuse, C=Cosine, T=Tangent

• listen tanx=p/b

that means oppositeside to the angle x ratio with the adjacent side...

• I am here to learn as much as anything else and was wondering why this would even be called algebra as it sounds more like geometry to me! I'd like to know why it is considered algebra 'cause if it is, I have much more to learn than I ever thought!

• tg X= sinX/cosX