Answer:
- L+M = 90°
- sin(42°) = 0.66913 = MN/LM
- sin(48°) = 0.74314 = LN/LM
Explanation:
The first box can be filled by adding up the two angles:
m∠L +m∠M = 42° +48° = 90°
You don't really have to go to that trouble, because you already know that the sum of the two acute angles in a right triangle is 90°. (They are complements of each other.)
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Since no side lengths are given, you need to use your calculator to find the sines of these angles, if a numerical value is required. If a literal ratio is required, the mnemonic SOH CAH TOA reminds you that ...
Sin = Opposite/Hypotenuse
sin(L) = MN/LM = sin(42°) ≈ 0.66913
sin(M) = LN/LM = sin(48°) ≈ 0.74314