Question

A boat is heading towards a lighthouse, whose beacon-light is 126 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 6^{\circ} ∘ , before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 22^{\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 887 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.

In this problem, the vertical change is of 126 feet.

At point A, the angle is of 6º, while the horizontal position is of $x_A$, hence:

$\tan{6^\circ} = \frac{126}{x_A}$

$x_A = \frac{126}{\tan{6^\circ}}$

$x_A = 1198.8$

At point B, the angle is of 22º, while the horizontal position is of $x_B$, hence:

$\tan{22^\circ} = \frac{126}{x_B}$

$x_B = \frac{126}{\tan{22^\circ}}$

$x_B = 311.9$

Hence, the distance in feet is of:

$d = x_A - x_B = 1198.8 - 311.9 \approx 887$

More can be learned about the slope concept at brainly.com/question/18090623