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Sponge. Hand in vocabulary book. Complete your vocabulary quiz. Complete your sponge quiz (7 th block only). Hand in assessments and homework to receive any objective test that need to be completed. Look over new project. Finding the Hypotenuse. January 6, 2012. Agenda.
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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.
Finding the Hypotenuse January 6, 2012
Agenda • Sponge Quiz/Vocabulary Quiz • Objective Test • Discuss agenda • Find the hypotenuse of a triangle
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.
Finding the Hypotenuse • Remember that the longest side of a right triangle is called the hypotenuse. Hypotenuse Leg Leg
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
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 ______
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.
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
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.
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.
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.
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.
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.
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.
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
