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Question

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agent0smith · Answer

Hmm, have you learned how to use the cosine rule? That seems like a possible (but tedious) way to solve it.

It seems like there should be a simpler way to do this, but I don't store a lot of geometry knowledge...

anonymous · Answer

Note that for 11., the two triangles share 2 sides. Only their bases are different, i.e. one has a base of 8 and the other has a base of 7. Now we know that the angle opposite the side with length 8 is 32 degrees. We also know that the other triangle that shares 2 sides has a base of 7, which is just 1 less than 8. This means that the angle x- 6, opposite the side with length 7 is going to be smaller (not by much) than 32 degrees. We also know that the angle will be greater than 0. Hence the range will be given by: $$\bf 0 < x-6<32 \implies 6 < x < 38$$You can evaluate number 12 in a similar manner. @maymay_69

anonymous · Answer

@MayMay_69

agent0smith · Answer

@genius12 Q12 is essentially the same problem - if you put the two triangles together, they share the middle side.

anonymous · Answer

I'm not sure whether the use of triangle inequality theorem is necessary here or if I was required to do more. My answer is based on my judgment of the question.

@agent0smith I know.

anonymous · Answer

Like I said: "You can evaluate number 12 in a similar manner."

agent0smith · Answer

Ah, i did not read that far :P my bad.

anonymous · Answer

lol @agent0smith

agent0smith · Answer

Ah that makes more sense. I don't remember the triangle inequality theorem, I assumed we had to somehow solve it using (possibly) the cosine rule... I didn't get too far.

agent0smith · Answer

But now it seems pretty obvious what they're asking for.