5.+Theorem+Applications

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Your answer should include a) identifying numerical information and show understanding of what the problem is asking you to solve, b) explanation of why certain information is needed to solve the problem and explanation of your procedures for solving the problem, and c) correct solution with explanation of what the answer means. Problems 1-5 are worth 3 points, see rubric.
 * __Application Problems__**

1. Find the length (to the nearest foot) of the cable shown below, use the right triangle formed by the tower, the bridge surface, and the cable.

2. A ladder that is 15 feet long is placed against a wall. The bottom of the ladder is 5 feet from the wall. To the nearest foot, how far up the wall does the ladder reach?

3. The skyscrapers are connected by a skywalk with support beams. You can use the Pythagorean Theorem to find the approximate length of each support beam. Each support beam forms the hypotenuse of a right triangle. The right triangles are congruent, so the support beams are the same length.

4. In slow-pitch softball, the distance between consecutive bases is 65 feet. The pitcher’s plate is located on a line between second base and home plate, 50 feet from home plate. How far is the pitcher’s plate from second base? Justify your answer.

5. To determine whether the corner of a shelf is actually a right angle, a carpenter uses a ruler and a pencil to make a mark at 3 inches along one side of the shelf and at 4 inches along the other. The carpenter takes a measurement and is satisfied that the corner is a right angle. What distance did the carpenter measure? Why does the carpenter’s method work?

Rubric for application problems 1-5, 3 points each


 * || **Distinguished – 1.0 ** || **Proficient – 0.75 ** || **Apprentice - 0.5 ** || **Novice - 0.25 ** ||
 * Understands the Problem || Identifies special factors that influences the approach before starting the problem || Understands the problem || Understands enough to solve part of the problem or to get part of the solution || Doesn't understand enough to get started or make progress ||
 * Uses Information Appropriately

Applies Appropriate Procedures || Explains why certain information is essential to the solution and what procedures are appropriate for the problem || Uses all appropriate information correctly, and applies completely appropriate procedures || <span style="font-family: 'Arial','sans-serif'; font-size: 8pt; margin: 0in 0in 0pt;">Uses some appropriate information correctly, and applies some appropriate procedures || <span style="font-family: 'Arial','sans-serif'; font-size: 8pt; margin: 0in 0in 0pt;">Uses inappropriate information and applies inappropriate procedures ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 8pt; margin: 0in 0in 0pt;">Answers the Problem || <span style="font-family: 'Arial','sans-serif'; font-size: 8pt; margin: 0in 0in 0pt;">Correct solution of problem and made a general rule about the solution or extended the solution to a more complicated solution || <span style="font-family: 'Arial','sans-serif'; font-size: 8pt; margin: 0in 0in 0pt;">Correct solution || <span style="font-family: 'Arial','sans-serif'; font-size: 8pt; margin: 0in 0in 0pt;">Copying error, computational error, partial answer for problem with multiple answers, no answer statement, answer labeled incorrectly || <span style="font-family: 'Arial','sans-serif'; font-size: 8pt; margin: 0in 0in 0pt;">No answer or wrong answer based upon an inappropriate plan ||