Question 1105131: In ΔABC, AC = BC, CD ⊥ AB with D ∈ AB , AB = 4 in, and CD = √3 in. Find AC.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! looks like you have an isosceles triangle.
since it's an isosceles triangle, then the perpendicular from C to D bisects the base and angles ACD and BCD are congruent.
bisecting the base means that AD = DB.
since AB = 4 inches long, then AD and DB are each 2 inches long.
since CD is part of triangles ACD and BCD, both of which are right triangles, you can find the length of either AC or BC by using the pythagorus formula of hypotenuse squared = the sum of each leg squared.
AD and CD are legs of triangle ACD.
CD and DB are legs of triangle BCD.
this makes the hypotenuse of each triangle equal to the square root of (2^2 + sqrt(3)^2) which makes the hypotenuse equal to square root of 7.
the sides of your triangle are:
AC = 7
BC = 7
AB = 4
CD = sqrt(3)
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