Question

A boat is heading towards a lighthouse, where Meena is watching from a vertical

Answer 1

Answer:

  245 ft

Step-by-step explanation:

The geometry of the problem can be modeled by a right triangle in which Meena's height is the side opposite the angle of depression, and the distance to the boat is the side adjacent to the angle of depression. The mnemonic SOH CAH TOA reminds us of the relation ...

  Tan = Oppsite/Adjacent

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The more useful trig function for this problem is the inverse of the tangent function, the cotangent. Using that function, we have ...

  cot(angle) = (distance to boat)/(Meena's height)

Then the distance to the boat is ...

  distance to boat = (Meena's height)×cot(angle)

The change in distance from A to B is then ...

  A -B = (120 ft)(cot(18°) -cot(44°))

  = (120 ft)(3.0777 -1.0355) ≈ 245.06 ft

The distance from point A to point B is about 245 feet.