Question

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

Answer 1

Using the slope concept, it is found that the distance from point A to point B is of 116 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:

• 107 feet above the water, hence a vertical change is of 107.

• The horizontal position is $x_A$, which we want to find.

• The angle of depression is of 20º.

Hence:

$\tan{20^{\circ}} = \frac{107}{x_A}$

$x_A\tan{20^{\circ}} = 107$

$x_A = \frac{107}{\tan{20^{\circ}}}$

$x_A = 294$

At point B:

• 107 feet above the water, hence a vertical change is of 107.

• The horizontal position is $x_B$, which we want to find.

• The angle of depression is of 31º.

Hence:

$\tan{31^{\circ}} = \frac{107}{x_B}$

$x_B\tan{31^{\circ}} = 107$

$x_B = \frac{107}{\tan{31^{\circ}}}$

$x_B = 178$

The distance is:

$D = |x_A - x_B| = |294 - 178| = 116$

The distance from point A to point B is of 116 feet.

You can learn more about the slope concept at brainly.com/question/26125945