Sponge

1. Sponge • Hand in vocabulary book. • Complete your vocabulary quiz. • Complete your sponge quiz (7th block only). • Hand in assessments and homework to receive any objective test that need to be completed. • Look over new project.

2. Finding the Hypotenuse January 6, 2012

3. Agenda • Sponge Quiz/Vocabulary Quiz • Objective Test • Discuss agenda • Find the hypotenuse of a triangle

4. Finding the Hypotenuse • Remember that the past few days we have been working with the Pythagorean Theorem which states: • a2 + b2 = c2 • Today we will apply this formula to find the length of the hypotenuse.

5. Finding the Hypotenuse • Remember that the longest side of a right triangle is called the hypotenuse. Hypotenuse Leg Leg

6. Finding the Hypotenuse • Write the following steps • Step 1: Write a2 + b2 = c2 • Step 2: Replace a with __ • Step 3: Replace b with __ • Step 4: Evaluate the squares • Step 5: Add • Step 6: Find the square root

7. Finding the HypotenuseExample: 1 • Pythagorean Theorem a2 + b2 = c2 • Replace a with _______ and b with ________ • Evaluate 122 and 162 • Add 144 and 256 • Find the square root of both side to undo c2 • The equation has two solutions, ________ and _________. However, the length of a side must be positive. So, the hypotenuse is ______

8. Finding the HypotenuseExample 2 • Pythagorean Theorem a2 + b2 = c2 • Replace a with _______ and b with ________ • Evaluate • Add • Find the square root of both side to undo c2 • The hypotenuse is _________ feet long.

9. Finding the HypotenuseExample 3 • Pythagorean Theorem a2 + b2 = c2 • Replace a with _______ and b with ________ • Evaluate • Add • Find the square root of both side to undo c2 • The hypotenuse is _________ inches long

10. Finding the HypotenuseExample 4 • Pythagorean Theorem a2 + b2 = c2 • Replace a with _______ and b with ________ • Evaluate • Add • Find the square root of both side to undo c2 • The hypotenuse is _________ feet long.

11. Finding the hypotenuseExample 5 • a= 18 in, b = 80 in, c = ? • This time we are not given a picture, but we can still follow the same steps to find c.

12. Finding the hypotenuseExample 5 • a= 18 in, b = 80 in, c = ? • Pythagorean Theorem a2 + b2 = c2 • Replace a with _______ and b with ________ • Evaluate • Add • Find the square root of both side to undo c2 • The hypotenuse is _________ inches long.

13. Finding the hypotenuseExample 6 • a = 24 ft, b = 70 ft, c = ? • Pythagorean Theorem a2 + b2 = c2 • Replace a with _______ and b with ________ • Evaluate • Add • Find the square root of both side to undo c2 • The hypotenuse is _________ feet long.

14. Finding the hypotenuseExample 7 • a = 7 m, b = 24 m, c = ? • Pythagorean Theorem a2 + b2 = c2 • Replace a with _______ and b with ________ • Evaluate • Add • Find the square root of both side to undo c2 • The hypotenuse is _________ meters long.

15. Finding the hypotenuseExample 8 • a = 5 cm, b = 12 cm, c = ? • Pythagorean Theorem a2 + b2 = c2 • Replace a with _______ and b with ________ • Evaluate • Add • Find the square root of both side to undo c2 • The hypotenuse is _________ centimeters long.

16. Exit Slip • The side lengths of a right triangle are 5, 12 and 13. How do you know that the length of the hypotenuse is 13? Explain • Fill in the blanks for each step to find the missing hypotenuse length of the triangle below (sides of 12 mm and 16 mm). • 122 + __2 = c2 • __ + 256 = c2 • __ = c2 • __ = c