Answer:
about 35.18
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