1 233 Finding Zeros Gregory is the proud new owner of a sailboat the Cutty Snark Its the most common type of sailboat a Bermuda sloop and has two sails a headsail in front and a mainsail in back The mainsail is in the shape of a right triangle On the ID: 336640
Download Presentation The PPT/PDF document "Check it out!" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Check it out!
1
2.3.3:
Finding ZerosSlide2
Gregory
is the proud new owner of a sailboat, the
Cutty
Snark. It’s the most common type of sailboat, a Bermuda sloop, and has two sails: a headsail in front, and a mainsail in back. The mainsail is in the shape of a right triangle. On the Cutty Snark, one leg of the triangular mainsail is 31 feet shorter than the other. The longest side of the mainsail is 41 feet. In order to make the proper adjustments, Gregory must know the area of the sail.What is the length of the short leg in terms of x? Using the Pythagorean Theorem, what quadratic equation relates the three sides of the mainsail? What are the factors of this equation? What is the area of the mainsail?
2
2.3.3:
Finding ZerosSlide3
What
is the length of the short leg in terms of x?
The short leg is 31 feet shorter than the other leg. Let x represent the unknown length of the longer leg.
The
shorter leg is (x – 31) feet. 32.3.3: Finding ZerosSlide4
Using
the Pythagorean Theorem, what quadratic equation relates the three sides of the mainsail?
Substitute each length of the sail into the Pythagorean Theorem and simplify.
The quadratic equation 2
x2 – 62x – 720 = 0 relates the three sides of the mainsail.42.3.3:
Finding Zeros
a
2
+
b
2
=
c
2Pythagorean Theorem
(x)2 + (x – 31)2 = (41)2Substitute values for each side length: x for a, (x – 31) for b, and 41 for c.
x2 + x2 – 62x + 961 = 1681Square the binomial.
2
x
2
– 62
x
– 720 = 0
Subtract 1,681 from both sides and combine like terms. Slide5
What
are the factors of this equation?
Factor out the greatest common factor, which is 2. 2(x2 – 31x – 360) = 0
Find
two numbers whose product is –360 and whose sum is –31.The numbers are –40 and 9. Write these numbers as factors. The factors are (x – 40) and (x + 9). 52.3.3: Finding ZerosSlide6
What
is the area of the mainsail?
Use the factors to determine the area of the mainsail.The factors can be used to determine the actual lengths of each leg of the triangular mainsail.
Set each factor equal to 0 and solve for
x. x + 9 = 0 x = –9 One possible length of x is –9. x – 40 = 0 x = 40 The other possible length of x is 40. 62.3.3: Finding ZerosSlide7
The factor (
x + 9) results in a negative length (–9) and, therefore, is not a possible leg length of the sail.
The factor (x – 40) results in a length of 40 feet. The other leg is 31 feet shorter than this length, or
9
feet. Use the area formula for a triangle, , to calculate the area of the sail.A = 180The area of the sail is 180 ft.2 72.3.3: Finding Zeros