idk how to do this geometry question

[acoustic socket]

please help

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[acoustic socket]

im new to the topic (its about cosine and sine law)

and also the applications of different trig methods.

im just a little lost on this question.

[modest violet]

probably the easiest way to do this will be to find <CED with some law of sines, then <ECD

[acoustic socket]

then what tho

[modest violet]

did you get that far

[acoustic socket]

i somehow got smth like 44.2 but the book says 34.2

[acoustic socket]

idk if its me just being dumb or smth

is it possible to help calculate it or smth? idk. prolly a brain malfunction on my part.

[modest violet]

book is correct

what steps do you have

[acoustic socket]

well basically cuz angle EDC is 50, CD is 10

don't i use sine law to prove that angle CED is like 106.xx

cuz it's obtuse?

then you can find angle ECA = 90-(180-106.xx-50 )

then use cos law to find AE

and then sin law to find CAE and thus EAB

then use the area = 1/2 ab sinC

to solve the area.

[modest violet]

yeah

[acoustic socket]

i just can't seem to figure out which step was the wrong one...

i know im wrong,i just dunno where it started...

[modest violet]

this is definitely a bit overcomplicated

once you have <ECD = 180 - 106.xx - 50

drop perpendicular from E onto CD
say it reaches CD at point F
then <CFE has a right angle at F, by definition
and so you can find EF
then height of triangle AEB will be 10 - EF

[acoustic socket]

oh

OH

wait but how do u solve for EF

?

[modest violet]

because EF/CE is sin(<ECF) = sin(<ECD)

[acoustic socket]

sorry im new to this chapter, and i kinda suck at geometry....

[modest violet]

opposite over hypotenuse

[acoustic socket]

ah

gotcha

[modest violet]

i think you will find creating right triangles even when diagram does not have them is quite helpful

[acoustic socket]

oic

wow

i've just successfully wasted 30 minutes of my life

trying to solve this lol

thanks 🙂

[modest violet]

np

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[acoustic socket]

+close