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welcome to math worksheet org today what
I want to show you how to do is solve a
problem using right triangle
trigonometry so what we're going to be
talking about here is when we're given a
right triangle how can we solve for a
missing value a couple things I want to
remind you of is when we have a right
triangle how can we label it well first
of all we know that a right triangle is
gonna be a right triangle by one of its
angles is going to be 90 degrees well
usually we label that with the little
box now I'll be right triangle offer
that 90 degree angle are the two legs of
the triangle one is what we call it
Jason and once we're gonna call the
opposite side I'll get two I would call
those those in just a second the sine
length that's directly across for you 90
degree angle a lot of times you say that
the 90 degree angle points towards it is
what we call our high pops now if we
have an angle
I'll besides our 90 degree angle we call
that angle usually theta and theta is
going to help us determine which side
links which of our legs are adjacent and
our opposite side so the opposite side
is the side that is opposite of your
angle theta
your adjacent side is going to be the
side length that connects your angle
theta and your right angle now when
using right triangle trigonometry we
have some functions that we can use to
solve for our missing side links and
that's what we have our sine cosine and
tangent now these are all functions that
are going to use the ratios of our side
lengths they are given our triangle so
right here we have a problem where I
have a right triangle my angle has been
given which is 15 degrees my hypotenuse
is 10 and my side length which I know is
going to be at my Jason side it's going
to be X so what I'm going to want to use
is I'm going to want to use these
functions to solve for my missing angle
X now I look at these three functions
that I needed a turn which is going to
be the best function to choose well I
know that sign represents
my opposite over my hypotenuse so I know
my opposite I Maya promise in this
problem I am not given the opposite side
so it would not be useful for me to use
sine tangent I'm also going to use the
opposite side so it will not be useful
to use tangent
however for using the cosine I'm only
going to have to know the adjacent and
the hypotenuse so what I can do is I'm
going to use my jacent my hypotenuse and
my angle theta to plug it into my cosine
function
so I'll write cosine rather of theta I
know my angle theta is 15 degrees equals
the ratio of my Jaison side over my
hypotenuse so my Jaison side of this
triangle is going to be x over 10 now it
would be very helpful to have a
scientific calculator so you can
evaluate evaluate what cosine 15 degrees
is cosine of 15 degrees is going to be
when you round it will be point 9 7
equals x times 10 so now to find my
value of X what do you can do is get the
X by itself being isolated so right now
I have my bearable being divided by 10
so to get rid of divided by 10 I simply
need to multiply the left and right side
by 10 so then there I multiply my 10 I'm
going to move my decimal one more over
so I have nine point seven equals x so
looking at my triangle I have now just
determined what the Jason's out of my
Angeles or I'm sorry Jason side the side
of my triangle which is nine point seven
so that's how you solve this missing
triangle thank you
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