In Triangle ABC, AD is median. If AB is 8, BC is 18, AD is 7, find AC
Since AD is the median
BD = DC = 9
In ∆ABD, let ∢BDA = Ø
by the cosine law:
8^2 = 9^2 + 7^2 - 2(9)(7)cosØ
cosØ = .5238
Ø = 58.4°
the ∢ADC = 121.59°
now in ∆ADC
AC^2 = 49 + 64 - 2(7)(8)cos121.59
= 171.666667
AC = 13.102 or 13
To find the length of AC in Triangle ABC, we can first find the length of BD using the median property.
Given that AD is a median, we know that it divides side BC into two congruent segments. Since AD = 7, BD will also be equal to half of BC: BD = BC/2 = 18/2 = 9.
Now, we can use the Pythagorean theorem to find the length of AC. In right triangle ABC, AC is the hypotenuse, and AB and BC are the other two sides.
Using the Pythagorean theorem, we have:
AC^2 = AB^2 + BC^2
Substituting the given values, we have:
AC^2 = 8^2 + 18^2
= 64 + 324
= 388
To find AC, we take the square root of both sides of the equation:
AC = sqrt(388)
≈ 19.7
Therefore, the length of AC in Triangle ABC is approximately 19.7 units.