Answer x = 743.2 feet from shore Explanation Given information: Boating: The Ponce de Leon lighthouse in St. Augustine, Florida, is the second tallest brick tower in the United States. It was built in 1887 and rises 175 feet above the sea level. Calculation: The angle of depression is not actually one of the angle we need. We need the angle in the triangle which is 90 ∘ − 13.25 ∘ (I changed the minutes to degrees, 15/60 = 0.25). We are dealing with the opposite and adjacent sides so this is a tangent problem. tan 76.75 ∘ = x 175 tan 76.75 ∘ × 175 = x x = 4.2468 × 175 x = 743.2 feet from shore .

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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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.

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Question

Chapter 5.4, Problem 9CFU

To determine

How far from the shore is a motorboat if the angle of depression from the top of the lighthouse is 13∘15' ?

Expert Solution & Answer

Answer to Problem 9CFU

x=743.2 feet from shore

Explanation of Solution

Given information: Boating: The Ponce de Leon lighthouse in St. Augustine, Florida, is the second tallest brick tower in the United States. It was built in 1887 and rises 175 feet above the sea level.

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.4, Problem 9CFU

The angle of depression is not actually one of the angle we need.

We need the angle in the triangle which is 90∘−13.25∘ (I changed the minutes to degrees, 15/60 = 0.25).

We are dealing with the opposite and adjacent sides so this is a tangent problem.

tan76.75∘=x175tan76.75∘×175=xx=4.2468×175x=743.2 feet from shore.

Chapter 5.4, Problem 8CFU

Chapter 5.4, Problem 10E

Chapter 5 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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