The lengths of two sides of a parallelogram are 24 cm and 15 cm. one angle measures 120°. find the length of the longer diagonal.
a) 13.3 cm
b) 34.1 cm
c) 177.5 cm
d) 1161 cm

B) 34.1 cm

Step-by-step explanation:

The longer diagonal is longer than either side, but shorter than their sum. The only answer choice in the range of 24–39 cm is choice B.

You are given sufficient information to use the Law of Cosines to find the diagonal length. If we call it "c", then the angle opposite that diagonal is the larger of the angles in the parallelogram: 120°. The law of cosines tells you ...

c^2 = a^2 +b^2 -2ab·cos(C)

Here, we have a=24, b=15, C=120°, so ...

c^2 = 24^2 +15^2 -2·24·15·cos(120°) = 576 +225 +360 = 1161

c = √1161 ≈ 34.073 . . . . cm

Rounded to tenths, the diagonal length is 34.1 cm.

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