Before Class Work

Name TG 1/30/06 Before Class Work Two runners leave the city of Watertown at noon. One runner travels north and the other travels east. Suppose the northbound runner is running 6 miles per hour and the eastbound runner is running 5 miles per hour. Make a table that shows the distance each runner has traveled and the distance between the two runners after 1 hour, 2 hours, and 3 hours. 6 mph 5 mph Watertown

Looking For Pythagoras Investigation 4.3 Finding the Perimeter

Problem 4.3 In the diagram below, some lengths and measures are given. Use this info and what you have learned in this unit to help you find the perimeter of triangle ABC. Explain your work. C 30 A B D 8

Problem 4.3 Follow-Up Find the area of triangle ABC. Explain your reasoning. C 30 A B D 8

Problem 4.3 Follow-Up Find the areas of triangles ACD and triangle BCD. Explain your reasoning. C 30 A B D 8

30-60-90 Right Triangle The leg opposite the 30 degree angle is always ½ of the length of the hypotenuse. 30 6 60 3

45-45-90 Right Triangle A B The triangles are congruent. 45 45 In a 45-45-90 right triangle, two sides are equivalent. 45 45 C D

Problem 4.3 In the diagram below, some lengths and measures are given. Use this info and what you have learned in this unit to help you find the perimeter of triangle ABC. Explain your work. C 60 30 30 60 A B D 8

Problem 4.3 The leg opposite the 30 degree angle is always ½ of the length of the hypotenuse. C 16 60 30 30 60 A B D 8

Problem 4.3 The leg opposite the 30 degree angle is always ½ of the length of the hypotenuse. C 16 30 60 A B 32

Problem 4.3 Use the Pythagorean Theorem. C Is this length 768? 16 x 16 = 256 16 32 x 32 = 1,024 1,024 – 256 = 768 30 60 A B 32 768 = 27.7

Problem 4.3 Find the area of ABC. C What two numbers do we use for area? 27.7 16 30 60 A B 32

Problem 4.3 Find the area of ABC. C What two numbers do we use for area? 27.7 16 16 x 27.7 = 443.2 30 60 A B 32 Cut 443.2 in half = 221.6

Problem 4.3 Follow-Up Find the areas of triangles ACD and triangle BCD. Explain your reasoning. C 16 27.7 30 A B D 8 32

Problem 4.3 Follow-Up Find the areas of triangles ACD and triangle BCD. Explain your reasoning. C 16 27.7 30 A B D 8 24 32

Problem 4.3 Follow-Up Area of triangle ACD. C Find CD first. 16 27.7 16 x 16 = 256 192 8 x 8 = 64 256 – 64 = 192 30 A B D 8 24 192 = 13.9 32

Problem 4.3 Follow-Up Area of triangle ACD. C 8 x 13.9 = 111.2 16 27.7 Cut 111.2 in half 13.9 ½ of 111.2 = 55.6 30 Area of ACD = 55.6 A B D 8 24 32

Problem 4.3 Follow-Up Area of triangle BCD. C 24 x 13.9 = 333.6 16 27.7 Cut 333.6 in half 13.9 ½ of 333.6 = 166.8 30 Area of ACD = 166.8 A B D 8 24 32

HW Problem 2, Page 47 15 m 15 m 45 45 1000 m How long, to the nearest tenth of a meter, is the cable for the Sky Breaker ride?

HW Problem 3, Page 47 2 feet What is the tallest tree that can be braced with a 25-foot wire staked 15 feet from the base of the tree? 25 feet 15 feet

HW Problem 4, Page 48 How tall is the Beaumont Tower? Explain how you found your answer. 60 5 feet 58 feet

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Before Class Work