Section 2.5 Formulas and Applications from Geometry 147 Student Check 3 a. t = d r b. h = 3V b c. b1 = 2A - b2h h d. y = 4x - 8 e. y=- 4 5 x - 4 Student Check 4 a. The angle measures 20°. b. The angle measures 60°. c. The angle measures 30°. Student Check 5 a. The measures of the angles are 56° and 124°. b. The angle measure is 110°. Student Check 6 a. The angles in the triangle have measures of 85°, 75°, and 20°. b. The angles in the triangle have measures of 100°, 30°, and 50°. SUMMARY OF KEY CONCEPTS 1. Evaluating formulas is similar to evaluating algebraic expressions. Substitute the given values for the appropriate variables and simplify. Use the order of operations to simplify the resulting expression. The goal in this objective is to find the value of the missing variable. To find this value, we will either simplify an expression or solve an equation. 2. Perimeter, area, and circumference formulas should be memorized for the basic shapes (triangle, square, rectangle, and circle). If the dimensions of the figure are given, we can find the perimeter, area, or circumference by substituting the given dimensions. We can also find the dimensions of the figure if the perimeter, area, or circumference are provided as well. 3. To solve a formula for a specified variable is to rewrite the equation so that a different variable is isolated to one side. No substitutions are made in this process. We simply apply the addition and multiplication properties of equality to solve for a different variable. 4. Complementary angles and supplementary angles are two angles whose sum is 90° and 180°, respectively. The most common error is misrepresenting the unknown form of these angles. If a is the measure of the angle, then 90 - a is the measure of the complement and 180 - a is the measure of the supplement. 5. Straight angles measure 180°. Vertical angles are formed when two lines intersect. Vertical angles are equal in measure. 6. The sum of the measures of the angles in a triangle is 180°. GRAPHING CALCULATOR SKILLS We can use the calculator to approximate expressions involving π. 1. 673 2π 6 3 4 ( 2 2nd ) ENTER So, 673 2π is approximately equal to 107.11. 2. π (107.1)2 2nd ( 1 ) x2 ENTER 1 So, π (107.1)2 is approximately equal to 36,035.36. Write About It! Use complete sentences to explain the meaning of each term. 1. Formula 2. Perimeter 3. Area 4. Circumference 5. Complementary angles 6. Supplementary angles 7. Straight angle 8. Vertical angles Determine if each statement is true or false. If a statement is false, explain why. 9. When 8x - y = 16 is solved for y, we get y = -8x. 10. If the measure of an angle is a, then the measure of the angle’s supplement is a - 180. 11. If the radius of a circle is 10 ft, the area of the circle is 100π ft2. 12. If angles with measures (4a - 5)° and (2a + 20)° are vertical angles, then 4a - 5 + 2a + 20 = 180. �� ���������������� �������� EXERCISE SET
hendricks_beginning_algebra_1e_ch1_3
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