Answer:
b. 4.0 cm
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the ratio of the adjacent side to the hypotenuse is given by the cosine of the angle:
Cos = Adjacent/Hypotenuse
cos(35°) = NL/NK
NL = NK·cos(35°)
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Similarly, it reminds you that the ratio of the opposite side to the hypotenuse is given by the sine function:
Sin = Opposite/Hypotenuse
sin(53°) = NM/NL
NM = NL·sin(53°)
Substituting from the first triangle, we have ...
NM = NK·cos(35°)·sin(53°)
NM = (6.1 cm)(0.81915)(0.79864)
NM ≈ 3.991 cm
MN ≈ 4.0 cm
