Purchase Solution

# Applications of Trigonometry and Matrices

Not what you're looking for?

Trigonometric Applications and Matrices
---------------------------------------------

Researchers at the National Interagency Fire Center in Boise, Idaho coordinate many of the firefighting efforts necessary to battle wildfires in the western United States. In an effort to dispatch firefighters for containment, scientists and meteorologists attempt to forecast the direction of the fires. Some of this data can be expressed as matrices. Help them solve the following problems.

1. A ranger in fire tower A spots a fire at a direction of 295 degrees. A ranger in fire tower B, located 45 miles at a direction of 45 degrees from tower A, spots the same fire at direction of 255 degrees. How far from tower A is the fire? From tower B?

2. In mountain communities, helicopters drop chemical retardants over areas which approximate the shape of an isosceles triangle having a vertex angle of 38 degrees. The angle is included by two sides, each measuring 20 ft. Find the area covered by the chemical retardant.

3. The chemical retardants are freight shipped from a warehouse. A shipping crate that weights 450 kilograms is placed on a loading ramp that makes an angle of 30 degrees with the horizontal. Find the magnitude of the components of the crate's weight perpendicular and parallel to the incline.

4. The meteorologists at the National Interagency Fire Center had pizza delivered to their operations center. Their lunch consisted of pizza, milk and gelatin. One slice of cheese pizza contains 290 calories, 15g of protein, 9g of fat, and 39g of carbohydrates. One-half cup of gelatin dessert contains 70 calories, 2g of protein, 0g of fat, and 17g of carbohydrates. One cup of whole milk contains 150 calories, 8g of protein, 8g of fat, and 11g of carbohydrates.
Write 1 x 4 matrices P, G, and M that represent the nutritional values of each food. Find 3P+2G+2M and tell what the entries represent.

##### Solution Summary

Solutions are provided along with two diagrams. Each trigonometric identity used to solve these problems is clearly stated. Solution is easy to understand.

##### Solution Preview

Following is the text part of the solution. Equations, diagrams, graphs and special characters will not appear correctly here. Please see the attached file for complete solution.

===========================================================

Trigonometric Applications and Matrices
---------------------------------------------

Researchers at the National Interagency Fire Center in Boise, Idaho coordinate many of the firefighting efforts necessary to battle wildfires in the western United States. In an effort to dispatch firefighters for containment, scientists and meteorologists attempt to forecast the direction of the fires. Some of this data can be ...

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.