Given: △ A K M , K D ⊥ A M, △ A K M , K D ⊥ A M Find: K D

Question

Given:   △  A  K  M  ,  K  D  ⊥  A  M,  △  A  K  M  ,  K  D  ⊥  A  M Find:   K  D

minnegodks · Accepted Answer

1    2    ⋅  |  A  K  |  ⋅  |  K  M  |  ⋅  sin  ⁡  (  ∠  A  K  M  )  =      1    2    ⋅  |  A  M  |  ⋅  |  K  D  |    |  K  D  |  =                |      A      K          |      ⋅          |      K      M          |      ⋅      sin      ⁡      (      ∠      A      K      M      )                  |      A      M          |          |  A  M  |  =        |    A    K              |      2        +      |    K    M              |      2        −    2    ⋅      |    A    K      |    ⋅      |    K    M      |    ⋅    cos    ⁡    (    ∠    A    K    M    )      ∴     ,  |  K  D  |  =                |      A      K          |      ⋅          |      K      M          |      ⋅      sin      ⁡      (      ∠      A      K      M      )                  |      A      K                    |        2            +          |      K      M                    |        2            −      2      ⋅          |      A      K          |      ⋅          |      K      M          |      ⋅      cos      ⁡      (      ∠      A      K      M      )             Substituting the respective values, we get 5.023, to 3 decimal places.

Ryan Reynolds · Accepted Answer

Area =             1      2        |  A  K  |  |  K  M  |  s  i  n  ∠  A  K  M  =            1      2        |  A  M  |  |  K  D  |  |  A  K  |,   |  K  M  | are given. Also by The Law of Cosines, you can find   |  A  M  |,  thus you can find   |  K  D  |.

Given: △ A K M

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