Thread: Triangles

Triangle ABC is isosceles with AC=BC=13 and AB=10. M and N are the feet of the perpendiculars from A and B to Bc and AC respectively. Find Bn.



Could someone please help me? Thank you!

Hello, Coach!

Triangle ABC is isosceles with
are the feet of the perpendiculars from , resp.
Find

Code:

                C
                *
               /|\
              / | \
             /  |  \
            /   |   \
        13 /    |    \ 13
          /   12|     \
         /      |      \
        /       |       \
       /        |        \
      * - - - - + - - - - *
      A    5    D    5    B

We see that
. . From Pythagorus: .

Code:

                C
                *
               /|\
              / | \
             /  |  \
            /   |   \
        N  /    |    \
          *     |     \
         /    * |      \
        /       | *     \
       /        |     *  \
      * - - - - + - - - - *
      A         D         B

We have similar right triangles: .
. . (They share .)

Code:

                                            C
                                            *
                                           /|
                                          / |
                                         /  |
                                        /   |
          N                        13  /    | 12
          *                           /     |
         /    *                      /      |
        /         *                 /       |
       /              *            /        |
      * - - - - - - - - - *       * - - - - *
      A        10         B       A    5    D

Hence, we have: .


Therefore: .