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 meteologists attempts to forecast the direction of the fires . Some of this data can be expressed as matrices . Help 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 .
Trigonometry application word problems are solved in this solution, which is provided in an attached Word document.