(a) Answer θ = 31.4 ∘ Explanation Given information: National Monuments: In 1906, Teddy Roosevelt designated Devils Tower National Monument in northeast Wyoming as the first national monument in the United States. The tower rises 1280 feet above the valley of the Bell Fourche River. Calculation: This will be a tangent problem as the sketch shows. We are looking for an angle which means it is an arc function problem. In this case we know the opposite and adjacent sides so it is a tangent problem. tan − 1 1280 2100 = θ θ = 31.4 ∘ (b) To determine To find: How long is the shadow when the angle of elevation of the sun is 38 ∘ ? Answer 1638 feet Explanation Given information: National Monuments: In 1906, Teddy Roosevelt designated Devils Tower National Monument in northeast Wyoming as the first national monument in the United States. The tower rises 1280 feet above the valley of the Bell Fourche River. Calculation: If the angle of elevation to the sun is 38 ∘ we want the shadow length. So this is a tan problem. tan 38 ∘ = 1280 shadow length shadow length = 1280 tan 38 ∘ shadow length = 1638 feet (c) To determine To find: How far is the hiker from the base of Devils Tower, if a person at the top of Devils Tower sees a hiker at an angle of depression of 65 ∘ ? Answer 597 feet Explanation Given information: National Monuments: In 1906, Teddy Roosevelt designated Devils Tower National Monument in northeast Wyoming as the first national monument in the United States. The tower rises 1280 feet above the valley of the Bell Fourche River. Calculation: Remember the angle of depression is from the horizontal down. The angle in our triangle is the complement of that or 90 ∘ − 65 ∘ = 25 ∘ tan 25 ∘ = distance from monument 1280 distance from monument = 1280 × tan 25 ∘ distance from monument = 596.9 feet

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 5.5, Problem 14CFU

(a)

To determine

To find: The angle of elevation of the sun, if the shadow of the tower is 2100 feet long at a certain time.

(a)

Expert Solution

Answer to Problem 14CFU

θ=31.4∘

Explanation of Solution

Given information: National Monuments: In 1906, Teddy Roosevelt designated Devils Tower National Monument in northeast Wyoming as the first national monument in the United States. The tower rises 1280 feet above the valley of the Bell Fourche River.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.5, Problem 14CFU , additional homework tip 1

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.5, Problem 14CFU , additional homework tip 2

This will be a tangent problem as the sketch shows. We are looking for an angle which means it is an arc function problem. In this case we know the opposite and adjacent sides so it is a tangent problem.

tan−112802100=θθ=31.4∘

(b)

To determine

To find: How long is the shadow when the angle of elevation of the sun is 38∘ ?

(b)

Expert Solution

Answer to Problem 14CFU

1638 feet

Explanation of Solution

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.5, Problem 14CFU , additional homework tip 3

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.5, Problem 14CFU , additional homework tip 4

If the angle of elevation to the sun is 38∘ we want the shadow length.

So this is a tan problem.

tan38∘=1280shadow lengthshadow length=1280tan38∘shadow length=1638 feet

(c)

To determine

To find: How far is the hiker from the base of Devils Tower, if a person at the top of Devils Tower sees a hiker at an angle of depression of 65∘ ?

(c)

Expert Solution

Answer to Problem 14CFU

597 feet

Explanation of Solution

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.5, Problem 14CFU , additional homework tip 5

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.5, Problem 14CFU , additional homework tip 6

Remember the angle of depression is from the horizontal down. The angle in our triangle is the complement of that or 90∘−65∘=25∘

tan25∘=distance from monument1280distance from monument = 1280×tan25∘distance from monument=596.9 feet

Chapter 5.5, Problem 13CFU

Chapter 5.5, Problem 15E

Chapter 5 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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