Question

Please help with problem

Answer 1

9514 1404 393

Answer:

• ∠CAE ≈ 16.7°
• DF ≈ 5.3

Step-by-step explanation:

a) Angle CAE can be found using the tangent relation.

  tan(∠CAE) = CE/AE

  tan(∠CAE) = 6/20

  ∠CAE = arctan(6/20) ≈ 16.7°

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b. The length of DF can be found using the law of cosines.

  DF² = FA² +DA² -2·FA·DA·cos(A)

  DF² = 14² +10² -2·14·10·cos(16.7°) ≈ 27.8086

  DF ≈ √27.8086

  DF = 5.3