Question on Exam which I would like to know the answer to

[da micah]

The instructions were:
AE = 4
EC = 8
AD = 5
DB = 5
AED = 90
Find the length of BC

 

[Deleted member 4993]

The instructions were: AE = 4 EC = 8 AD = 5 DB = 5 AED = 90
Find the length of BC

Are you supposed to seek external help in Exam?

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about this assignment.

Do you know the laws of sines and cosines for a triangle?

If yes - please state those.

 

[bZNyQ7C2]

I guess I'm not supposed to help, so I won't. But the OP does not need the sine or cosine laws for this problem.

 

[Steven G]

Can you show us what you tried? Can you label anything else in the figure? How can we help you if you give us nothing to help you with?

 

[Dr.Peterson]

I guess I'm not supposed to help, so I won't. But the OP does not need the sine or cosine laws for this problem.

There is nothing wrong in offering suggestions. In this case, I think the law of cosines is the most obvious approach (to me), but I'm sure there are other ways, and if the OP doesn't know that law, other ideas may be needed. Go ahead and offer additional hints.

My very first thought was to see whether angle B might be a right angle, which would have made it very easy; but it turns out not to be (by similar triangles).

 

[Dr.Peterson]

That's a bigger "hint" than I had in mind; giving a piece of the answer and asking why is beyond "hint". If I were you, I might have just asked what would happen if you constructed a perpendicular from B to AC.

But in fact I had missed the fact that a question had been asked about permission to ask for help on an exam, which hadn't been answered. I was (too optimistically?) taking it to mean "a past exam", since surely one wouldn't boldly ask for the answer to a current take-home exam ...

And my hint was, I hoped, small enough anyway.

 

[Steven G]

@Dr.Peterson ... The OP said this question came from an exam. Our moderator Mr. Khan asked if s/he was allowed to seek external help. So I'm not sure whether offering hints in this case is appropriate. If it is, I'll be glad to.

Here's my solution. I'm sure there are other solutions, but I would bet this is the solution the OP was meant to find.
View attachment 14658

Yes, drawing BF is the best way to do this problem after finding out B is not a right angle.