Question

Determine the length of MN to the nearest tenth of a centimetre.

Select one or more:
a. 3.0 cm
b. 4.0 cm
c. 2.8 cm
d. 2.1 cm

Answer 1

b. 4.0 cm

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