so the first thing we can do
is label the triangle
right taylor this isn't that bad right
just label the triangle
hypotenuse here's for my angle this
would be the adjacent side
and here is my opposite side
now looking at this
all right
you guys can now see that
um i don't have anything for my adjacent
but i have opposite over hypotenuse so
who was helping me out josh do you
remember what trigonometric function
deals with opposite and hypotenuse
sine
so i can write sine of x equals the
opposite over the hypotenuse
but here's the problem ladies and
gentlemen
we don't know what x is
okay
now a couple things i
you guys are in the really early stages
of inverses and so forth so i don't want
to get too detailed into this but one of
my questions that i'd say is um
devin
if i was gonna solve this what would be
my next step
right so how would i how would i solve
this what would my next step do you know
what would be my next step
minus four right he asking me man yeah
would be
division good
all right now if i have x squared equals
16
what do i do if you don't know if i can
open up to the gallery
what is my inverse operation
can we take it or someone else
take it
huh
not division kevin
so what's the opposite of squaring
square root
you take the square
root
right these are what we call inverse
operations the inverse operation of
squaring is the square root so if i had
the square root of 5
equal 10
how would i undo the square root of
something
square it right
now so what i want you guys to
understand
is the inverse operation of squaring you
don't like divide or you don't divide by
like the square root sign
okay that's not the operation of square
rooting you have to square it so what i
want you guys to understand is
we're taking the sine of this angle
it's the sine of the angle it's not sine
times x so we cannot just divide by x
that's not what we're doing we need to
take the opposite of sine
all right we need to do the opposite
operation of the sine function so stop
that please
so what is the opposite right it took
you guys a while just to figure out what
the opposite of x squared was what the
heck is the opposite of sine without
giving you guys too much information or
getting too confusing
the opposite operation for sine is just
what we call sine inverse
okay and it looks like that
you can go in your calculator and if you
have a scientific calculator above the
sign button should be the sign inverse
button so you're going to want to hit
second sign
and then you can just put in parentheses
6 divided by 18
or reduce that to 1 3 and what i get is
19.47
make sure you're in degree mode
okay i can show you i can help you out
now the next thing is they're not asking
us though for x they're asking us for b
is it pretty easy though to do 19 minus
your answer minus 90 degrees i'm sorry
crap
180
minus your answer minus 90.
and therefore i can get this to be 70
70.53
what's confusing
what which part
did you understand how to label adjacent
opposite and hypotenuse do you
understand how i could only use the sine
function
okay do you understand how i plugged in
the opposite side in for opposite and 18
right and then i don't know what x is
right so i do you understand how i
plugged it into this equation okay
all i want you to understand is if i
said x plus 4 equals 10 you subtract 4
right to solve for x so if i have the
sine of x there's no like add subtract
multiply divide you have to take the
inverse sine that is the opposite of
sine is the inverse sine just like the
opposite of adding 4 is subtracting 4.
the opposite of multiplying by 4 is
dividing by 4. the opposite of squaring
x is square rooting x the opposite of
sine is inverse sine so then all you do
you have to have a calculator all you do
is take the inverse of that sign
and inverse of 6 over 18 and that's the
number you get
that is my angle
now if i want to find angle b i take 180
right because all the angles in a
triangle add up to 180. so i say 180
minus
19.47
minus
90 degrees equals my angle b
but i can also do this one other way i'm
going to do this really quickly
for justice
real quickly what about if i just wanted
to find b directly
why go through all this weight to find x
what if i just want to find b directly
well what information do i have
6 is that 6 my opposite side or my
adjacent side robert
for angle b
you're adjacent and what is 18 is that
my hypotenuse or am i opposite
it's always your hypotenuse right so
therefore i can say
so since i'm doing adjacent over
hypotenuse
cosine
of
my angle x which i'm pretending i don't
know
is equal to 6 over 18. so therefore x
equals cosine inverse
of 6 over 18.
yep i'll show you in just a second so
then i just do second cosine
of parenthesis
8 or i'm sorry 6 divided by 18. and when
doing that i get 70.53
done
okay