Final answer:
Using the Pythagorean theorem, the length of AC in triangle ABD with given sides BC and CD is calculated to be approximately 6.15 inches.
Step-by-step explanation:
To find the length of AC in triangle ABD, where altitude AC intersects the right angle at vertex A and given that BC = 2.3 inches and CD = 5.7 inches, we will use the Pythagorean theorem. The altitude AC divides the right triangle ABD into two smaller right triangles ABC and ACD. Since we are given the lengths of the legs of triangle ACD, we can find the length of the hypotenuse AC.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the lengths of the other two sides (BC and CD). Therefore:
AC2 = BC2 + CD2
AC2 = (2.3 inches)2 + (5.7 inches)2
AC2 = 5.29 + 32.49
AC2 = 37.78
AC = √37.78
AC = 6.145, which rounds to 6.15 inches.
Thus, the length of AC is approximately 6.15 inches.