University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

426

Pages:

1
Author:

numcore694sxk

Mini-Lecture 8.6 Radical Equations and Problem Solving Learning Objectives: 1. Use the Pythagorean formula to solve problems. 2. Use the distance formula. 3. Solve problems using formulas containing radical. Examples: 1. Use the Pythagorean Theorem to find the length of the unknown side of each right triangle. Give an exact answer and a two-decimal-place approximation. a) b) 7 6 14 8 Find the length of the unknown side of each right triangle with sides a, b, and c, where c is the hypotenuse. Give an exact answer and a two-decimal-place approximation. c) a = 15, b = 20 d) b = 18, c = 82 e) a = 20, c= 28 2. Use the distance formula to find the distance between the points given. a) (4,2), (5,8) b) (-4,-6), (-1,5) c) (-8,6), (8,-6) 3. Solve. Give a two decimal place approximation. a) A baseball diamond is a square measuring 90 feet on each side. What is the distance from first base to third base? b) A firefighter places a 37-foot ladder 9 feet from the base of the wall of a building. Will the top reach a window ledge that is 35 feet above the ground? c) Denise set up a volleyball net in her backyard. One of the poles, which forms a right angle with the ground, is 7 feet high. To secure the poles, he attached a rope from the top of the pole to a stake 3 feet from the bottom of the pole. Find the length of the rope. d) Cindy and Dan leave home at the same time. Dan drives eastward at 30 miles per hour, while Cindy drives south at 50 miles per hour. Find how far apart they are to the nearest mile after 3 hours. Teaching Notes: • • • Most students can use Pythagorean Theorem when the triangle is in the form of 1a). Many students get confused when the triangle is rotated as in 1b). Remind students to locate the right angle; the side directly across from the right angle is the hypotenuse. Remind students to draw a picture, label a diagram, etc. when solving applications. Again, always locate the right angle, which will lead to identifying the hypotenuse. Answers: 1a) 2 58 , 15.23; 1b) 2b) 57 , 7.55; 1c) 25; 1d) 80; 1e) 8 6 , 19.60; 2a) 130,11.40 ; 2c) 2; 3a) 127.28 ft. 3b) yes; 3c) 7.62 ft.; 3d) 175 mi. 37, 6.08 ;