Answer:
(b) 5
Explanation:
You want the length of the short diagonal in a parallelogram with sides 4 and 6 and acute angle 55°.
Law of Cosines
The law of cosines will tell you the length of the side opposite the given angle in a triangle with two sides and an included angle known.
c² = a² +b² -2ab·cos(C)
c² = 4² +6² -2·4·6·cos(55°) = 16 +36 -48·0.57358 ≈ 24.47
c ≈ √24.47 ≈ 5
The length x of the diagonal is about 5 units, choice B.
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Additional comment
The long diagonal is about 9 units. It is opposite the supplementary 125° angle.
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