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A boat is heading towards a lighthouse, whose beacon-light is 108 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 8^{\circ}
∘
, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 16^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.

Respuesta :

Using the slope concept, it is found that the distance from point A to point B is of 392 feet.

What is a slope?

  • The slope is given by the vertical change divided by the horizontal change.
  • It's also the tangent of the angle of depression.

At point A:

  • The vertical change is of 108.
  • The horizontal change is the position [tex]x_A[/tex], that we want to find.
  • The angle is of 8º.

Hence:

[tex]\tan{8^\circ} = \frac{108}{x_A}[/tex]

[tex]x_A = \frac{108}{\tan{8^\circ}}[/tex]

[tex]x_A = 768.6[/tex]

At point B:

  • The vertical change is of 108.
  • The horizontal change is the position [tex]x_B[/tex], that we want to find.
  • The angle is of 16º.

Hence:

[tex]\tan{16^\circ} = \frac{108}{x_B}[/tex]

[tex]x_B = \frac{108}{\tan{16^\circ}}[/tex]

[tex]x_B = 376.6[/tex]

Then, the distance is:

[tex]d = x_A - x_B = 768.6 - 376.6 = 392[/tex]

The distance from point A to point B is of 392 feet.

You can learn more about the slope concept at https://brainly.com/question/26342863

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