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EMBED Equation.DSMT4  Step 2: Square and add each number as directed by the theorem.  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Step 3: Take the square root of each side to solve for c.  EMBED Equation.DSMT4  Example 2: Solve for a leg when given the hypotenuse and the other leg. A right triangle has a hypotenuse that measures 10 inches and one of the legs measures 6 inches. Find the length of the other leg. Step 1: Substitute known values into Pythagorean theorem.  EMBED Equation.DSMT4  Step 2: Square each number as directed by the theorem.  EMBED Equation.DSMT4  Step 3: Subtract from both sides to isolate the variable.  EMBED Equation.DSMT4  Step 4: Take the square root of each side to solve for the variable.  EMBED Equation.DSMT4  Instructor's Script Comparing and Contrasting The Math or program area instructor should fill in this area by comparing academic math problems to lab area problems. The instructor should describe ways that career and technical program math is similar to or different from the academic math that occurs in the PA Core Math standard or on Keystone related exams. Common Mistakes Made By Students Incorrectly identifying a, b, and c: Students often confuse the hypotenuse with one of the legs or incorrectly substitute values into the equation. To avoid this problem recognize that the diagonal often is used to describe a hypotenuse. Label your hypotenuse right away by quickly identifying the right angle and marking the side opposite the right angle as the hypotenuse. Inability to manipulate the equation to solve for a or b: Solving for the hypotenuse is much simpler than solving for a leg of a right triangle. Students need to be given many opportunities to solve for all the variables in the Pythagorean Theorem. Inability to recognize the Pythagorean Theorem in multiple contexts: The Pythagorean Theorem appears in many contexts in standardized testing. Sometimes a test question will describe a right triangle and ask the student to solve for the missing side. Other times, the right triangle is drawn and the student must solve for the missing side. In many cases, a more complex picture is drawn and the student must use the Pythagorean Theorem to solve part of the problem. In these cases, it is not obvious that the Pythagorean Theorem is needed and the student must be able to select and use the theorem.  CTE Instructors Extended Discussion The CTE instructor may add comments here describing the importance of this math skill in relationship to the program task, or note common problems which students have when making the computations. Problems Career and Technical Math Concepts SolutionsProgram relevant problemAllow work space hereProgram relevant problemAllow work space hereProgram relevant problemAllow work space hereProblems Related, Generic Math Concepts SolutionsA tent has two slanted sides that are both 5 feet long and the bottom is 6 feet across. What is the height of the tent in feet at the tallest point?Three sides of a triangle measure 9 feet, 16 feet and 20 feet. Determine if this triangle is a right triangle. On a baseball diamond, the bases are 90 feet apart. What is the distance from home plate to second base using a straight line?Problems PA Core Math Look SolutionsThe lengths of the legs of a right triangle measure 12 meters and 15 meters. What is the length of the hypotenuse to the nearest whole meter? In a right triangle ABC, where angle C is the right angle, side AB is 25 feet and side BC is 17 feet. Find the length of side AC to the nearest tenth of a foot.In the given triangle, find the length of a.  Problems Career and Technical Math Concepts SolutionsProgram relevant problemAllow work space hereProgram relevant problemAllow work space hereProgram relevant problemAllow work space hereProblems Related, Generic Math Concepts SolutionsA tent has two slanted sides that are both 5 feet long and the bottom is 6 feet across. What is the height of the tent in feet at the tallest point?a2 + b2 = c2 a2 + 32 = 52 a2 + 9 = 25 a2 = 16 a = 4Three sides of a triangle measure 9 feet, 16 feet and 20 feet. Determine if this triangle is a right triangle. a2 + b2 = c2 162 + 92 = 202 256 + 81 EMBED Equation.DSMT4 400 Therefore, it is not a right triangle.On a baseball diamond, the bases are 90 feet apart. What is the distance from home plate to second base using a straight line?902 + 902 = c2 8100 + 8100 = c2 16200 = c2  EMBED Equation.DSMT4 Problems PA Core Math Look SolutionsThe lengths of the legs of a right triangle measure 12 meters and 15 meters. What is the length of the hypotenuse to the nearest whole meter? EMBED Equation.DSMT4 In a right triangle ABC, where angle C is the right angle, side AB is 25 feet and side BC is 17feet. Find the length of side AC to the nearest tenth of a foot. EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4 In the given triangle, find the length of a.  EMBED Equation.DSMT4      Insert CTE Program Name here (insert CIP code here) T-Chart Originated June 2009 CC.2.3.8.A.3 Reviewed June 2015  PAGE \* MERGEFORMAT 1 A B C c a b a = leg b = leg c = hypotenuse Pythagorean Theorem: a2 + b2 = c2 B A C 26 in. a 10 in. A B C 25 ft. 17 ft. A C 26 in. a 10 in. 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