Question

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.

Answer 1

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 $x_A$, that we want to find.

• The angle is of 8º.

Hence:

$\tan{8^\circ} = \frac{108}{x_A}$

$x_A = \frac{108}{\tan{8^\circ}}$

$x_A = 768.6$

At point B:

• The vertical change is of 108.

• The horizontal change is the position $x_B$, that we want to find.

• The angle is of 16º.

Hence:

$\tan{16^\circ} = \frac{108}{x_B}$

$x_B = \frac{108}{\tan{16^\circ}}$

$x_B = 376.6$

Then, the distance is:

$d = x_A - x_B = 768.6 - 376.6 = 392$

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

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