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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