Find the measure of angle b
find x
find y

- cutiecomittee123

Find the measure of angle b
find x
find y

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- cutiecomittee123

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- jim_thompson5910

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- jim_thompson5910

using A as a reference angle, we can add these labels
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## More answers

- jim_thompson5910

find x and y using the trig ratios
then find angle B

- cutiecomittee123

okay

- cutiecomittee123

i need more pointers, @jim_thompson5910

- anonymous

still doing hw huh

- anonymous

angle b= 165

- anonymous

nvm

- anonymous

im tired.

- jim_thompson5910

how far did you get @cutiecomittee123 based on the info I posted?

- cutiecomittee123

no where lol let me try again

- cutiecomittee123

well i kind of took the easy way out and I just figured there are 180 degrees in a triangle and it is given 90+75 so i added them and got 165 then if you add 15 you get 180 so obviousely angle b is 15 degrees. but then to solve for x and y i can easily see that you just use the trig stuff

- jim_thompson5910

yes B = 15 degrees

- jim_thompson5910

how would you find x?

- cutiecomittee123

I am having a brain fart and cant remeber

- jim_thompson5910

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- jim_thompson5910

which angle do you want to use? A = 75? or B = 15?

- cutiecomittee123

well lets use B, and wouldnt you use cos because you would do adjacent over hypotenuse?
So it would be cos(15)=125/y

- jim_thompson5910

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- jim_thompson5910

cos(B) = adjacent/hypotenuse
cos(15) = 125/x
now solve for x

- cutiecomittee123

So wouldnt you take the inverse of both sides?

- cutiecomittee123

sorry for the super late replies i am also working on a power point.

- jim_thompson5910

it's ok, work on the powerpoint first and we can work on this later

- cutiecomittee123

Alright done with the presentation, lets do this:)

- jim_thompson5910

so you see how I got `cos(15) = 125/x` right?

- cutiecomittee123

yes

- jim_thompson5910

using a calculator, what is the value of `cos(15)` equal to (in terms of a decimal number)

- cutiecomittee123

cos(15)=.97

- jim_thompson5910

so what we really have is `0.97 = 125/x`
are you able to solve that for x?

- cutiecomittee123

hmm, multiply both sides by x?

- jim_thompson5910

then what

- cutiecomittee123

divide by .97

- jim_thompson5910

yes

- cutiecomittee123

on both sides

- jim_thompson5910

what is x equal to

- cutiecomittee123

x=128.87

- jim_thompson5910

ok so 125/0.97 = 128.87 is correct
it turns out that 125/(cos(15)) = 129.40952255126 is the more accurate answer
so it might be best to type into your calculator `125/(cos(15))`

- cutiecomittee123

okay cool got it, but why would you divide it form 125?

- jim_thompson5910

\[\Large \cos(15^{\circ}) = \frac{125}{x}\]
\[\Large \cos(15^{\circ})\color{red}{*x} = \frac{125}{x}\color{red}{*x}\]
\[\Large \cos(15^{\circ})\color{black}{*x} = \frac{125}{\cancel{x}}\color{black}{*\cancel{x}}\]
\[\Large \cos(15^{\circ})*x = 125\]
\[\Large \frac{\cos(15^{\circ})*x}{\color{red}{\cos(15^{\circ})}} = \frac{125}{\color{red}{\cos(15^{\circ})}}\]
\[\Large \frac{\cancel{\cos(15^{\circ})}*x}{\cancel{\cos(15^{\circ})}} = \frac{125}{\color{black}{\cos(15^{\circ})}}\]
\[\Large x = \frac{125}{\color{black}{\cos(15^{\circ})}}\]

- jim_thompson5910

So what I first did was multiply both sides by `x`
then I divided both sides by `cos(15)`

- cutiecomittee123

i see you just solved it like an algebraic equation, basic algebra

- jim_thompson5910

yeah if you have to, think of `cos(15)` as y
so you'd have y = 125/x
solving for x gives x = 125/y

- cutiecomittee123

okay woah, so now y=129.41 and then we can just use the pythagorean theorum to solve for x. so 129.41^2+125^2=x^
added together i get 32302.1396
the square root of that is 179.72796
so x=179.73

- jim_thompson5910

no, I let y = cos(15)
so y = 0.97 like you got, but it's best to leave the cos(15) part alone as it is

- jim_thompson5910

if you typed 125/cos(15) into a calculator, what do you get?

- cutiecomittee123

I get 129.41

- jim_thompson5910

yes, 125/cos(15) = 129.40952255126

- cutiecomittee123

which is what the side y is equal to

- jim_thompson5910

oh my bad, I picked y when y is already being used in the drawing

- cutiecomittee123

yeah lol oops. but yes I think we have it all figured out now. thanks so much!!!!

- jim_thompson5910

you're welcome

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