Good day students in this clip were going to be going over how to find the area of the triangle using trigonometry

Psalm let's go ahead and take a look at the formulas that we are going to be using to find the areas and then what

applied into the three examples okay so let's write down the formulas so there are three cases of three groups of cases

there were going to be looking at the first one is the SAS situation you have a side to side the included angle SAS the

formula for the area in this case is simply one half a be signed see okay where the included angle of your secant see

you see or another we can look at this is one half of the side as the side times the sign of the included angle which

is represented by a okay right so SAS is very easy because when you have an SAS situation all you simply do is plug in

the two sides and included angle into this equation and you're done okay when you have an SSS situation you cannot use

trigonometry for this you have to use a special formula known as he was formula for this case the area is given by the

square roots of the cemetery S times the semiperimeter minus a time the semi perimeter minus B time the semi. Minus C

okay you might wonder what is the semi perimeter of the semi perimeter is just what you gets when you added three sides

a plus B+ C and divided by of two write so this is the first case the street for the second case is also pretty

straightforward but what of if we have S S A S is a is equivalents to a SS which of the we want to look at it or if we

have him AAS which is equivalent to S AA what of if we have the situation is right here what the have these case is of

what you have to do is you have to convert these cases in twenty S A S situation using degrees loft sine circuit is

very convenient using law of science right and we convert these into an SAS situation then you simply use the SAS

formula to finish the problem off okay so these are the cases are going to be looking that's right to lets take a look

at question number one for question one with the fire of this triangle right here so let's leave all the sides the

relevant sites this is A so call this a this is B so call this b this is C utterly needs c in this problem you see wine

in minutes now recall SAS situation is very easy and direct right SSS requires the use of the of yours formulae and

then the other ones require more work so what's configuration do we have here can it is and what it is well let's say

we have assigned in the have an angle and have a site this is excellent because this is an SAS situation which requires

very little work because the have everything that we need okay right so let's Psalm right of the formula for the area

here so for number one the area is going to be one half S S sign a to two S's are a and D sign the included angle is C

okay Lenny partitioned my workspace here so we can get confused this is the region of area for the formula as camera

put my solutions to the left or right okay so now we have the formula written down now is going to apply the formula to

this triangles right so you have a is equal to one half a is of eleven p.m. thirteen sign one oh six okay and eighty

plug this in your calculator with the Iranian is to the nearest tenth your answer is going to be approximately sixty-

eight point seven square kilometers kilometer square right to that will be your area's right let's take a look at

question number two write so what situation do we have here all is label what the have we have a side the have an angle

in the have the angle okay this is a S AA or AAS situation right so what are we going to do here well we just require

some work as indicated earlier the we have Palm SS AAS our S AA we have to convert it into an SAS situation so we can

apply this formula okay so let's see him which side you want to find will depend on the angle that you want to use okay

so let's say we want to use SAS lets you want to find the site right here the site okay so let's label the triangle and

then we can add it isolate the side we want to find and express this using a variable right so this is Y this to be y

right here this is why in this side right here is going to be what's to side is going to be x okay so this is S AAS now

we have to use loft signs here in order to find little X right so you not to use loft signs will going to be outside in

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