1. Chapter 2 Section 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. Formulas and Applications from Geometry 1 1 4 4 3 3 2 2 2.52.5 Solve a formula for one variable, given values of the other variables. Use a formula to solve an applied problem. Solve problems involving vertical angles and straight angles. Solve a formula for a specified variable.

3. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Formulas and Applications from Geometry Many applied problems can be solved with formulas. A formula is an equation in which variables are used to describe a relationship. For example, formulas exist for geometric figures such as squares and circles, for distance, for money earned on bank savings, and for converting English measurements to metric measurements. The formulas used in this book are given on the inside covers. Slide 2.5 - 3 Formulas

4. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1 Objective 1 Slide 2.5 - 4 Solve a formula for one variable, given the values of the other variables.

5. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solve a formula for one variable, given the values of the other variables. Given the values of all but one of the variables in a formula, we can find the value of the remaining variable. In Example 1,we use the idea of area. The area of a plane (two-dimensional) geometric figure is a measure of the surface covered by the figure. Slide 2.5 - 5

6. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Find the value of the remaining variable. EXAMPLE 1 Using Formulas to Evaluate Variables Solution: Slide 2.5 - 6 The length of the rectangle is 38. Once the values of the variables are substituted, the resulting equation is linear in one variable and is solved as in previous sections.

7. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Objective 2 Use a formula to solve an applied problem. Slide 2.5 - 7

8. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Use a formula to solve an applied problem. Formulas are often used in applied problems. It is a good idea to draw a sketch when a geometric figure is involved. Examples 2 and 3 use the idea of perimeter. The perimeter of a plane (two-dimensional) geometric figure is the distance around the figure. For a polygon (e.g., a rectangle, square, or triangle), it is the sum of the lengths of its sides. We use the six steps introduced in the previous section. Slide 2.5 - 8

9. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 2 Solution: Let L = the length of the field, then L − 50 = the width of the field. Finding the Dimensions of a Rectangular Field The length of the field is 225 m and the width is 175 m. Slide 2.5 - 9 A farmer has 800 m of fencing material to enclose a rectangular field. The width of the field is 50 m less than the length. Find the dimensions of the field.

10. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley The longest side of a triangle is 1 in. longer than the medium side. The medium side is 5 in. longer than the shortest side. If the perimeter is 32 in., what are the lengths of the three sides? EXAMPLE 3 Solution: Let x − 5 = the length of the shortest side, then x = the length of the medium side, and x + 1 = the length of the longest side. Finding the Dimensions of a Triangle Slide 2.5 - 10 The shortest side of the triangle is 7 in., the medium side is 12 in., and the longest side is 13 in.

11. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4 Solution: Let b = the base of the triangle. Finding the Height of a Triangle Slide 2.5 - 11 The base of the triangle is 10 m. The area of a triangle is 120 m 2. The height is 24 m. Find the length of the base of the triangle.

12. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3 Objective 3 Solve problems involving vertical angles and straight angles. Slide 2.5 - 12

13. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solve problems involving vertical angles and straight angles. Now look at angles and. When their measures are added, we get 180°, the measure of a straight angle. There are three other such pairs of angles: and, and, and and. Slide 2.5 - 13 The figure below shows two intersecting lines forming angles that are numbered,,, and. Angles and lie “opposite” each other. They are called vertical angles. Another pair of vertical angles is and. In geometry, it is known that vertical angles have equal measures.

14. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 5 Solution: Finding Angle Measures Slide 2.5 - 14 Find the measure of each marked angle in the figure. The two angle measures are 149° and 31°. The answer is not the value of x. Remember to substitute the value of the variable into the expression given for each angle.

15. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4 Objective 4 Solve a formula for a specified variable. Slide 2.5 - 15

16. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solve a formula for a specified variable. Sometimes it is necessary to solve a number of problems that use the same formula. For example, a surveying class might need to solve the formula for the area of a rectangle, A = LW. Suppose that in each problem area (A) and the length (L) of a rectangle are given, and the width (W) must be found. Rather than solving for W each time the formula is used, it would be simpler to rewrite the formula so that it is solved for W. This process is called solving for a specified variable or solving for a literal equation. In solving a formula for a specified variable, we treat the specified variable as if it were the only variable in the equation and treat the other variables as if they were numbers. We use the same steps to solve the equation for specified variables that we use to solve equations with just one variable. Slide 2.5 - 16

17. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 6 Solution: Solving for a Specified Variable Slide 2.5 - 17 or We use color for a specified variable. Try to circle or underline the variable you are solving for. Solve for t.

18. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 7 Solution: Solving for a Specified Variable Slide 2.5 - 18 or Solve for h.

19. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 8 Solution: Solving for a Specified Variable Slide 2.5 - 19 or Solve for t.

20. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solve for h. EXAMPLE 9 Solution: Solving for a Specified Variable Slide 2.5 - 20 or