Question

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 1

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 $x_A$, which we want to find.

• The angle of depression is of 21º.

Hence:

$\tan{21^{\circ}} = \frac{115}{x_A}$

$x_A\tan{21^{\circ}} = 115$

$x_A = \frac{115}{\tan{21^{\circ}}}$

$x_A = 299.6$

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

$\tan{45^{\circ}} = \frac{115}{x_B}$

$x_B\tan{45^{\circ}} = 115$

$x_B = \frac{115}{\tan{45^{\circ}}}$

$x_B = 115$

The distance is:

$d = |x_A - x_B| = |299.6 - 115| = 184.6$

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