Given: △klm lm=12, m∠k=60°, m∠m=45° find: perimeter of △klm. pls hep

  about 35.18

Step-by-step explanation:

The Law of Sines tells you the relationship between the sides and angles is ...

  KM/sin(L) = KL/sin(M) = LM/sin(K)

We are given LM and angles K and M.

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The sum of angles is 180°, so the remaining angle is ...

  ∠K +∠L +∠M = 180°

  60° +∠L +45° = 180° . . . . substitute the given angle values

  ∠L = 75° . . . . . . . . . . . . . . subtract 105°

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Now, we're in a position to find the missing side lengths.

  KM = sin(L)/sin(K)·LM = sin(75°)/sin(60°)·12 ≈ 13.38

  KL = sin(M)/sin(K)·LM = sin(45°)/sin(60°)·12 ≈ 9.80

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The perimeter of ΔKLM is ...

  P = KL +KM +LM

  P = 9.80 +13.38 +12.00

  P = 35.18

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