Example 4 the formula for the curved surface area s

This preview shows page 19 - 21 out of 50 pages.

EXAMPLE 4 The formula for the curved surface area S of a right circular cone of altitude h and with base of radius r is S = . Solve for r 2 . Solution This equation is quadratic in form. If we let y = r 2 , then we have By the quadratic formula we have the following: Since y = r 2 , we have Student Practice 4 The formula for the number of diagonals d in a polygon with n sides is d = Solve for n . 570571 Solving Problems Requiring the Use of the Pythagorean Theorem A very useful formula is the Pythagorean Theorem for right triangles. PYTHAGOREAN THEOREM If c is the length of the longest side of a right triangle and a and b are the lengths of the other two sides, then a 2 + b 2 = c 2 . The longest side of a right triangle is called the hypotenuse. The other two sides are called the legs of the triangle. EXAMPLE 5 (a) Solve the Pythagorean Theorem a 2 + b 2 = c 2 for a . (b) Find the value of a if c = 13 and b = 5. Solution Page 19 of 50 Print | Beginning & Intermediate Algebra 1/31/2014 ...
Image of page 19

Subscribe to view the full document.

PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted. (a) a 2 = c 2 b 2 Subtract b2 from each side. a, b , and c must be positive numbers because they represent lengths, so we use only the positive root, a = (b) Thus, a = 12. Student Practice 5 (a) Solve the Pythagorean Theorem for b . (b) Find the value of b if c = 26 and a = 24. There are many practical uses for the Pythagorean Theorem. For hundreds of years, it was used in land surveying and in ship navigation. So, for hundreds of years students learned it in public schools and were shown applications in su See if you can see how it is used in Example 6. Notice that it is helpful right at the beginning of the problem to draw a picture of the right triangle and label information that you know. 571572 EXAMPLE 6 The perimeter of a triangular piece of land is 12 miles. One leg of the triangle is 1 mile longer than the other leg. Find the length of each boundary of the land if the triangle is a right triangle. Solution 1. Understand the problem. Draw a picture of the piece of land and label the sides of the triangle. 2. Write an equation. We can use the Pythagorean Theorem. First, we want only one variable in our equation. (Right now, both c and x are not known.) We are given that the perimeter is 12 miles, so x + ( x + 1) + c = 12.Thus, c = 2 x + 11.By the Pythagorean Theorem, x 2 + ( x + 1) 2 = ( 2 x + 11) 2 . 3. Solve the equation and state the answer. x 2 + ( x + 1) 2 = ( 2 x + 11) 2 x 2 + x 2 + 2 x + 1 = 4 x 2 44 x + 1210 = 2 x 2 46 x + 1200 = x 2 23 x + 60By the quadratic formula, we have the following: 4. Check. Is the perimeter 12 miles? Is one leg 1 mile longer than the other?5 + 4 + 3 = 12 4 = 3 + 1 Student Practice 6 The perimeter of a triangular piece of land is 30 miles. One leg of the triangle is 7 miles shorter than the other leg. Find the length of each boundary of the land if the triangle is a right triangle.
Image of page 20
Image of page 21
  • Fall '13
  • Quadratic equation, student practice

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern