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.
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.
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.