### Problem DescriptionA boat is heading towards a lighthouse, whose beacon light is 130 feet above the water. From point $ A $, the boat's crew measures the angle of elevation to the beacon, $ 13^\circ $, before they draw closer. They measure the angle of elevation a second time from point $ B $ at some later time to be $ 23^\circ $. Find the distance from point $ A $ to point $ B $. Round your answer to the nearest tenth of a foot if necessary.### Interactive Answer Submission**Answer:** ______________________ feet[Submit Answer Button]### Explanation:To solve this problem, one would typically use trigonometric relationships, specifically the tangent of the angles of elevation, to set up equations based on the given heights and distances. The difference in distances from the lighthouse at points $ A $ and $ B $ combined with the height of the lighthouse can be used to derive the unknown distance between the points.

Answered: Image /qna-images/answer/745a10a6-67e7-42c0-9601-6f4a69a03a0e.jpg

A boat is heading towards a lighthouse, whose beacon-light is ig6 feet above the water. From point A, the boat's crew measures the angle of elevation to the beacon, 13, before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 22. Find the distance from point A to point B. Round your answer to the nearest tenth of a foot if necessarv

A boat is heading towards a lighthouse, whose beacon-light is ig6 feet above the water. From point A, the boat's crew measures the angle of elevation to the beacon, 13, before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 22. Find the distance from point A to point B. Round your answer to the nearest tenth of a foot if necessarv

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

### Problem Description

A boat is heading towards a lighthouse, whose beacon light is 130 feet above the water. From point $ A $, the boat's crew measures the angle of elevation to the beacon, $ 13^\circ $, before they draw closer. They measure the angle of elevation a second time from point $ B $ at some later time to be $ 23^\circ $. Find the distance from point $ A $ to point $ B $. Round your answer to the nearest tenth of a foot if necessary.

### Interactive Answer Submission

**Answer:** ______________________ feet

[Submit Answer Button]

### Explanation:

To solve this problem, one would typically use trigonometric relationships, specifically the tangent of the angles of elevation, to set up equations based on the given heights and distances. The difference in distances from the lighthouse at points $ A $ and $ B $ combined with the height of the lighthouse can be used to derive the unknown distance between the points.

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