Transcript The TANgent ratio

Leon Funchess

Okay, so when you have a right triangle, like so
For angles A and B, the ratio of the opposite
side to that angle to the adjacent side of that
angle always stays the same, no matter what
the measure of the angle. That ratio is the
TANGENT RATIO.
The writing above is
how you would write
the tangent ratio out, if
you used the example to
the right. You could
also shorten it to be:
The diagram above shows
which sides to use to
determine the tangent
ratio.
Writing the ratio is very simple… you
just have to follow the formula
mentioned on the previous page, ------>
but you have you sub in whatever the
angle is for A.
This one I’ll put up for you, but only because its your first time.
Notice things like how the order flipped when you changed angles… but also note that the size of angle T or U doesn’t matter… it’ll still be opposite/adjacent.
By using the side lengths and/or the angles, you
can find out various variables in a right triangle
that is given to you in a problem.
So let’s do this one together. Let’s start off by naming this
angle X. to find W, you need to write out the equation
first. tanX=opposite/adjacent. So to fill it in, you know
that 10 is adjacent angle X, and w is opposite to it. And
you also know that angle X = 54 degrees. So you fill
everything in: tan54=w/10. then you simplify: 10tan54=w.
then you put that into your calculator (SET IT TO
RADIAN!!!!!!!!!!!!) and you should get about 13.76.
For each one of the figures, figure out the
value of W. Then Write out the tangent ratio
for each of the triangles’ angles A and B.
1
B
A
A
B
2
Lol sike you can’t get them this
early!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Still not giving them to
you!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. W=1.89 ratios: tanA=1/1.89 tanB=1.89/1
2. W=3.85 ratios: tanA=2.5/3.85 tanB=3.85/2.5

Okay, so that section was pretty easy and
straightforward! I hope I helped you. If you
need more help, look in section 8.3 of the
textbook! Good luck on the finals everybody!