Exam 30: Applications and Models

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The designers of a water park are creating a new slide and have sketched some preliminary drawings.The length of the ladder is a = 26 feet,and its angle of elevation is 60º (see figure).? $The designers of a water park are creating a new slide and have sketched some preliminary drawings.The length of the ladder is a = 26 feet,and its angle of elevation is 60º (see figure).? ? Find the angle of depression \theta from the top of the slide to the end of the slide at the ground in terms of the horizontal distance d the rider travels. ?$ ? Find the angle of depression $\theta$ from the top of the slide to the end of the slide at the ground in terms of the horizontal distance d the rider travels. ?

(Multiple Choice)

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Question 41

An observer in a lighthouse a = 340 feet above sea level observes two ships directly offshore. The angles of depression to the ships are 4º and 6.5º (see figure).How far apart are the ships? Round your answer to one decimal place.

(Multiple Choice)

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Question 42

Find the distance y across the flat sides of a hexagonal nut (see figure). $r = 14$ cm Round your answer to two decimal places.? ?

(Multiple Choice)

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Question 43

Determine the angle between the diagonal of a cube and the diagonal of its base,as shown in the figure,where $a = 12$ .Round your answer to one decimal place.? ?

(Multiple Choice)

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Question 44

The angle of elevation of the sun is 26^o.Find the length,l,of a shadow cast by a tree that is 38 feet tall.Round your answer to two decimal places.

(Multiple Choice)

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Question 45

If $a = 12$ and $c = 18$ ,determine the value of A.Round to two decimal places.

(Multiple Choice)

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Question 46

After leaving the runway,a plane's angle of ascent is 17^o and its speed is 280 feet per second.How many minutes will it take for the airplane to climb to a height of 11,000 feet? Round your answer to two decimal places.

(Multiple Choice)

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Question 47

A plane is 52 miles west and 46 miles north of an airport.The pilot wants to fly directly to the airport.What bearing should the pilot take? Answer should be given in degrees and minutes.

(Multiple Choice)

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Question 48

A passenger in an airplane at an altitude of a = 20 kilometers sees two towns directly to the east of the plane.The angles of depression to the towns are 28º and 55º (see figure).How far apart are the towns? How far apart are the ships? Round your answer to one decimal place.

(Multiple Choice)

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Question 49

Determine whether the statement is true or false. ? The Leaning Tower of Pisa is not vertical,but if you know the angle of elevation ? to the top of the tower when you stand 20 feet away from it,you can find its height h using the formula? $h = 20 \tan \theta$ ?

(Multiple Choice)

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Question 50

A ladder 17 feet long leans against the side of a house.Find the height from the top of the ladder to the ground if the angle of elevation of the ladder is 80º.Approximate the answer to one decimal place.

(Multiple Choice)

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Question 51

You are holding one of the tethers attached to the top of a giant character balloon in a parade.Before the start of the parade the balloon is upright and the bottom is floating approximately 20 feet above ground level.You are standing approximately a = 100 feet ahead of the balloon (see figure).Round your answer to two decimal places. Find the height h of the balloon if the angle of elevation to the top of the balloon is 35º.

(Multiple Choice)

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Question 52

Showing 41 - 52 of 52

Exam 30: Applications and Models

An observer in a lighthouse a = 340 feet above sea level observes two ships directly offshore. The angles of depression to the ships are 4º and 6.5º (see figure).How far apart are the ships? Round your answer to one decimal place.​ ​

Find the distance y across the flat sides of a hexagonal nut (see figure). r=14r = 14r=14 cm Round your answer to two decimal places.? ?

Determine the angle between the diagonal of a cube and the diagonal of its base,as shown in the figure,where a=12a = 12a=12 .Round your answer to one decimal place.? ?

The angle of elevation of the sun is 26o.Find the length,l,of a shadow cast by a tree that is 38 feet tall.Round your answer to two decimal places.

If a=12a = 12a=12 and c=18c = 18c=18 ,determine the value of A.Round to two decimal places.

After leaving the runway,a plane's angle of ascent is 17o and its speed is 280 feet per second.How many minutes will it take for the airplane to climb to a height of 11,000 feet? Round your answer to two decimal places. ​

A plane is 52 miles west and 46 miles north of an airport.The pilot wants to fly directly to the airport.What bearing should the pilot take? Answer should be given in degrees and minutes.

A passenger in an airplane at an altitude of a = 20 kilometers sees two towns directly to the east of the plane.The angles of depression to the towns are 28º and 55º (see figure).How far apart are the towns? How far apart are the ships? Round your answer to one decimal place.​ ​

Determine whether the statement is true or false. ? The Leaning Tower of Pisa is not vertical,but if you know the angle of elevation ? to the top of the tower when you stand 20 feet away from it,you can find its height h using the formula? h=20tan⁡θh = 20 \tan \thetah=20tanθ ?

A ladder 17 feet long leans against the side of a house.Find the height from the top of the ladder to the ground if the angle of elevation of the ladder is 80º.Approximate the answer to one decimal place. ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Polar Equations of Conics

Graphs of Polar Equations

Filters

An observer in a lighthouse a = 340 feet above sea level observes two ships directly offshore. The angles of depression to the ships are 4º and 6.5º (see figure).How far apart are the ships? Round your answer to one decimal place.

Find the distance y across the flat sides of a hexagonal nut (see figure). $r = 14$ cm Round your answer to two decimal places.? ?

Determine the angle between the diagonal of a cube and the diagonal of its base,as shown in the figure,where $a = 12$ .Round your answer to one decimal place.? ?

The angle of elevation of the sun is 26^o.Find the length,l,of a shadow cast by a tree that is 38 feet tall.Round your answer to two decimal places.

If $a = 12$ and $c = 18$ ,determine the value of A.Round to two decimal places.

After leaving the runway,a plane's angle of ascent is 17^o and its speed is 280 feet per second.How many minutes will it take for the airplane to climb to a height of 11,000 feet? Round your answer to two decimal places.

A passenger in an airplane at an altitude of a = 20 kilometers sees two towns directly to the east of the plane.The angles of depression to the towns are 28º and 55º (see figure).How far apart are the towns? How far apart are the ships? Round your answer to one decimal place.

Determine whether the statement is true or false. ? The Leaning Tower of Pisa is not vertical,but if you know the angle of elevation ? to the top of the tower when you stand 20 feet away from it,you can find its height h using the formula? $h = 20 \tan \theta$ ?

A ladder 17 feet long leans against the side of a house.Find the height from the top of the ladder to the ground if the angle of elevation of the ladder is 80º.Approximate the answer to one decimal place.