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In ΔDEF, d = 440 inches, f = 410 inches and ∠F=120°. Find all possible values of ∠D, to the nearest 10th of a degree.

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There are two solutions for the triangle DEF: ∠ D₁ ≈ 68.3°, ∠ D₂ ≈ 111.7°.

How to find all possible values of a triangle by law of sines

In this question we have a triangle with two known sides and a known angle. By the law of sines we find the possible values of the angle D:

410/sin 120° = 440/sin D

Please notice that the sum of the internal angles of triangles equals 180°. Then,

sin D = (440/410) · sin 120°

sin D ≈ 0.929

There are two solutions for the triangle DEF: ∠ D₁ ≈ 68.3°, ∠ D₂ ≈ 111.7°.

To learn more on law of sines: https://brainly.com/question/17289163

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