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trigonometry !! a very tricky trick

hey there

regarding this problem

i know that i can use the cosine law and then the sine law to investigate whether the other ange must be 45 or not,,

but it takes alot of time and i kinda don't have that much time to solve a problem!!

i don't know if am overlooking other way of doing it??

Re: trigonometry !! a very tricky trick

I assume you are trying to show if this is true or false. You will have to use the cosine rule then the sine rule but to save yourself a bit of work think about whether the angle $\displaystyle \frac{\pi}{4}$ will be opposite the side with length 4 or 8.

Re: trigonometry !! a very tricky trick

You can solve this without the law of cosines if you note that 180 - 60 - 45 = 75 and 75 - 30 = 45.

Re: trigonometry !! a very tricky trick

emakarov,, i didn't really get how could that help me,,

may you please eleborate on that??

Re: trigonometry !! a very tricky trick

Let angle A be 60, AB = 4 and AC = 8. If angle C is 45, then angle B is 75. Draw the altitude BH. Then angle CBH is 45, i.e., BH = HC. Can you finish?

Re: trigonometry !! a very tricky trick

I understand the problem like this:

one side = 4

adjacent side = 8

angle between them = 60 deg

this is a half equilateral triangle. One angle is 90 deg and the other is 30 deg. I think pi/4 in the original question is incorrect, or the given sided lengths are not 4 and 8. The triangle of the original question does not exist.