given that BD and AC are perpendicular, what is the length of Ac?
AB=9.4
BD=7.9
BC=23.2
To find the length of AC, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Since BD and AC are perpendicular, they form a right triangle, with AC as the hypotenuse and BD and CD as the other two sides. We need to find the length of CD, which is the missing side in this right triangle.
To find CD, we can use the Pythagorean Theorem:
BD^2 + CD^2 = AC^2
Given that BD = 7.9, we can substitute this value into the equation:
7.9^2 + CD^2 = AC^2
Simplifying:
62.41 + CD^2 = AC^2
Since we don't have the value of AC, we cannot directly solve for CD using this equation. However, since we are given the lengths of AB and BC, we can use this information to find the missing values.
We can use the fact that triangle ABC is a right triangle to find the length of CD using the Pythagorean Theorem.
AC^2 = AB^2 + BC^2
Substituting the given values:
AC^2 = (9.4)^2 + (23.2)^2
AC^2 = 88.36 + 538.24
AC^2 = 626.6
Taking the square root of both sides, we can find the length of AC:
AC = √626.6
AC ≈ 25.03
Therefore, the length of AC is approximately 25.03.