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a A boat is heading towards a lighthouse, where Easton is watching from a vertical distance of 115 feet above the water. Easton measures an angle of depression to the boat at point A to be 21°. At some later time, Easton takes another measurement and finds the angle of depression to the boat (now at point B) to be 45°. Find the distance from point A to point B. Round your answer to the nearest tenth of a foot if necessary
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Answer :

Using the slope concept, it is found that the distance point A to point B is of 184.6 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:

  • 115 feet above the water, hence a vertical change is of 115.
  • The horizontal position is [tex]x_A[/tex], which we want to find.
  • The angle of depression is of 21º.

Hence:

[tex]\tan{21^{\circ}} = \frac{115}{x_A}[/tex]

[tex]x_A\tan{21^{\circ}} = 115[/tex]

[tex]x_A = \frac{115}{\tan{21^{\circ}}}[/tex]

[tex]x_A = 299.6[/tex]

At point B, the angle of depression is of 45º, hence:

[tex]\tan{45^{\circ}} = \frac{115}{x_B}[/tex]

[tex]x_B\tan{45^{\circ}} = 115[/tex]

[tex]x_B = \frac{115}{\tan{45^{\circ}}}[/tex]

[tex]x_B = 115[/tex]

The distance is:

[tex]d = |x_A - x_B| = |299.6 - 115| = 184.6[/tex]

The distance point A to point B is of 184.6 feet.

You can learn more about the slope concept at https://brainly.com/question/26153962

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