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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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5406ca01-59af-4525-aa74-c4d606a1cb55%2F745a10a6-67e7-42c0-9601-6f4a69a03a0e%2F3c64c32_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### 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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