Triangle ABC has side lengths AB = 231;BC = 160; and AC = 281: Point D is constructed on
the opposite side of line AC as point B such that AD = 178 and CD = 153: How to compute the distance
from B to the midpoint of segment AD
Hello, Mhmh96!
I assume you made a sketch . . .
Triangle ABC has side lengths AB = 231, BC = 160, and AC = 281.
Point D is constructed on the opposite side of line AC as point B such that AD = 178 and CD = 153.
Compute the distance from B to the midpoint of segment AD.
The diagram seems to be something like this.
Draw segment AD.Code:A o 178 * * * D * * o * * * 231 * * * * 281 * * * * * 153 * * * * * * * ** B o * * * * * * * * * o C 160
We find that: .
. . Hence: .
Now the diagram looks like this:
LetCode:A o * ** * 1 * * 178 * * * * * * * * * D 231 * * o * 281 * * * * * * * 2* 153 * * * * ** B o * * * * * * * o C 160
Law of Cosines:
Hence: .
Finally, the diagram looks like this:
Draw segmentCode:A o * * 89 * * M 78 * - - o * : * 89 * : * D o - - : - - o * : * * : * 153 * : * 153 * : * * : * * : * B o - - o - - o C 80 N 80
We see that
is the hypotenuse of right triangle
. . Hence: .
Therefore: .