Let ABC be a triangle with right angle C. The mid-point of the hypotenuse AB is twice as far from the side BC as it is from side AC. Find the length of the side AC, if AB = 10cm.

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- June 10th 2009, 03:42 AMVinsanityReal Hard Geo Question, need help
Let ABC be a triangle with right angle C. The mid-point of the hypotenuse AB is twice as far from the side BC as it is from side AC. Find the length of the side AC, if AB = 10cm.

- June 10th 2009, 04:23 AMI-ThinkWording
The wording of your question is a bit confusing. By the distance from midpoint of to and , do you mean the distance and as I have in my diagram?

This is how I did the calculation, if this is wrong, just let me know.

Answer

Let

As point, by letting and , we see that the triangles and are the same. Thus

,

Calculate for x with Pythagoras' theorem, and you'll find AC.

If my assumption is wrong, just let me know. - June 10th 2009, 04:29 AMVinsanity
wait give me a minute.

can you give your final answer as well. - June 10th 2009, 04:56 AMaidan
- June 11th 2009, 12:19 AMVinsanity
Why did you result using 2x in the first place

- June 11th 2009, 07:36 AMaidan
- June 12th 2009, 12:58 AMVinsanity
- June 12th 2009, 05:54 AMaidan
I can use trig because I had a very good 6th grade teacher. The teacher was adamant that we know what a trig function did -- not merely able to write that

*tangent = sine/cosine*or that*sine = opposite / hypotenuse*.

I can use trig because I practiced solving and creating trig problems.

There are many reasons that I can use trig, but those are the primaries.