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Tomtit [17]
3 years ago
13

Given: △KLM LM=12, m∠K=60°, m∠M=45° Find: Perimeter of △KLM. Pls hep

Mathematics
1 answer:
bagirrra123 [75]3 years ago
3 0

Answer:

  about 35.18

Step-by-step explanation:

The <em>Law of Sines</em> 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.

__

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°

__

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

__

The perimeter of ΔKLM is ...

  P = KL +KM +LM

  P = 9.80 +13.38 +12.00

  P = 35.18

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