Question

A boat heading out to sea starts out at Point A, at a horizontal distance of 1135 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 10 ∘ . At some later time, the crew measures the angle of elevation from point BB to be 3^∘ . Find the distance from point A to point B. Round your answer to the nearest tenth of a foot if necessary.

Answer 1

The angle between a line of sight of the lighthouse and a horizontal plane is referred to as an angle of elevation.

The distance between points A and B is 2683.7 feet

The question is illustrated with the attached image.

From the image, we have:

$\angle A = 10^o$

$\angle B = 3^o$

$AO = 1135$ ----- distance from the lighthouse.

First, we calculate the height of the lighthouse (TO).

This is calculated using the following tangent ratio

$\tan(A) = \frac{TO}{AO}$

So, we have:

$\tan(10) = \frac{TO}{1135}$

Solve for TO

$TO = 1135 \times \tan(10)$

$TO = 200.13$

Next, we calculate the distance from point B to the lighthouse (BO)

This is calculated using the following tangent ratio

$\tan(B) = \frac{TO}{BO}$

So, we have:

$\tan(3) = \frac{200.13}{BO}$

Solve for BO

$BO = \frac{200.13}{\tan(3)}$

$BO = 3818.71$

Distance AB is calculated by subtracting AO from BO.

$AB = BO - AO$

$AB = 3818.71 - 1135$

$AB = 2683.71$

$AB = 2683.7$ ---- approximated

Hence, the distance between points A and B is 2683.7 feet

Read more about angles of elevation at:

https://brainly.com/question/9817377