Question

Two boats are traveling toward a cliff that is 150 feet above sea level. When the two boats are exactly 200 feet apart, the boat closest to the cliff has an angle of elevation to the top of the cliff of 22 degree, as shown.

Answer 1

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Answer:

  14.71°

Step-by-step explanation:

The tangent relation can be helpful here.

  Tan = Opposite/Adjacent

With reference to the attached diagram ...

  tan(22°) = CD/DA = (150 ft)/DA

  tan(x) = CD/DB = (150 ft)/(DA +200 ft)

Substituting for DA, we find ...

  tan(x) = (150 ft)/((150 ft)/tan(22°) + 200 ft) ≈ 150/(371.26 +200) ≈ 0.262576

  x = arctan(0.262576)

  x ≈ 14.71°