Name. STAR CITY Math / Geometry / Special Right Triangles. Teacher Period. Use the diagram below to answer question 1.

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1 STAR CITY Math / Geometry / Special Right Triangles Use the diagram below to answer question 1. Name Teacher Period 2. The drawing shows the measurements in a section of a circular design. How long is the radius of the circle? 1. Lisa wants to lay a path of bricks from her house to her gazebo. She needs to find the distance from her house to the gazebo to determine how many bricks to buy. What is the distance of the diagonal from the house to the gazebo? Round to the nearest tenth. (Assume the area shown above is a square). A ft. B ft. C ft A. 10 cm B. 8.7 cm C. 7 cm D. 4.3 cm Use the figure below to answer question 3. D ft. 3. What is the value of x? A. 17 cm B cm C cm D. 34 cm 1

2 STAR CITY Math Geometry Special Right Triangles 4. Firemen are using a 75 ft. ladder extended to 70 ft. The ladder is positioned at a 60 angle with the horizontal of the truck. How many vertical feet is it from the top of the fire truck to the tip of the ladder? Use the diagram below to answer question 5. A ft. B ft. C ft. D. 35 ft. 5. To get from point A to point B, Kevin must avoid walking through a pond. To avoid the pond, he has to walk 33 meters west and 65 meters southeast. How many meters would be saved if he were to walk through the pond? A. 25 m B. 42 m C. 56 m D. 98 m 6. The hypotenuse of a triangle measures 10 inches. What is the area of the triangle, rounded to the nearest hundredth? A in. 2 B in. 2 C in. 2 D in. 2 2

3 STAR CITY Math Geometry Special Right Triangles 7. The diagram below shows some dimensions of Comiskey Baseball Park in Chicago, Illinois. A is home plate, C is dead center field, and DB is the segment from the left field foul-ball pole to the right field foul-ball pole. If the center fielder is standing at E, how far is he from home plate? Use the diagram below to answer question 9. A ft. B ft. C ft. D ft. 9. Susan and Jerilyn are standing at opposite corners of a square field. Susan wants to throw a ball to Jerilyn. How far does she have to throw it? Round to the nearest tenth. A ft. B ft. C ft. D ft. 8. Find the value of x and y. Use the figure below to answer question 10. A. x = 6 and y = 2 3 B. x = 4 3 and y = 12 C. x = 4 3 and y = 6 D. x = 3 and y = What is the approximate area of the sign if each side is 36 inches long? A. 108 in. 2 B. 561 in. 2 C. 648 in. 2 D. 1,296 in. 2 3

4 STAR CITY Math Geometry Special Right Triangles 11. The perimeter of the square below is 36. What is the length of the diagonal, x? Use the figure below to answer question 13. A. 6 B. 9 C. 6 2 D The diagonal crossbar of an old wooden gate has rotted. The gate is rectangular, 5 feet by 7 feet. About how long is the crossbar? A. 4.9 feet B. 8.6 feet C. 9.9 feet D feet 13. The Sailing Club participates in different races. One race course is in the design of an isosceles right triangle as shown above. A buoy is placed at each vertex of the course. The course starts at buoy 1, continues around buoy 2, then buoy 3, and then returns to buoy 1. If the length of the course from buoy 1 to buoy 2 is 3.5 nautical miles, what is the approximate distance from buoy 3 to buoy 1? A nm B nm C nm D nm 4

5 14. The Parks and Recreation Association is installing the playground equipment shown below at Ames Park. STAR CITY Math Geometry Special Right Triangles Find the distance from the base of the slide to the post. A feet B feet C. 24 feet D. 42 feet 5

6 STAR CITY Open-Response / Geometry / Special Right Triangles Name Teacher Period GEOMETRY OPEN-RESPONSE ITEM A A. The Titanic left port on April 10, When leaving Queenstown, the power of the Titanic broke the ropes of the docked S.S. New York and pulled it into it's wake. The two ships nearly collided. 1. If the ships had collided at their bows as diagramed below, what would have been the approximate distance between the sterns of the ships? Round your answer to the nearest foot. Show or explain all of your work. 2. On April 15, 1912 at 2:10 A.M., the Titanic tilted 45 as the bow was submerging. The stern rose out of the water as shown below. If 380 ft. of the Titanic was not submerged at this time, approximately how far above the water was the stern of the Titanic? Round your answer to the nearest foot. Show or explain all of your work. BE SURE TO LABEL YOUR RESPONSES 1 AND 2. 6

7 STAR CITY Name Student Answer Document / Geometry / Special Right Triangles Teacher Period A 7

8 GEOMETRY OPEN-RESPONSE ITEM A (T.2.G.4, T.2.G.5B) A. The Titanic left port on April 10, When leaving Queenstown, the power of the Titanic broke the ropes of the docked S.S. New York and pulled it into it's wake. The two ships nearly collided. 1. If the ships had collided at their bows as diagramed below, what would have been the approximate distance between the sterns of the ships? Round your answer to the nearest foot. Show or explain all of your work. 2. On April 15, 1912 at 2:10 A.M., the Titanic tilted 45 as the bow was submerging. The stern rose out of the water as shown below. If 380 ft. of the Titanic was not submerged at this time, approximately how far above the water was the stern of the Titanic? Round your answer to the nearest foot. Show or explain all of your work. BE SURE TO LABEL YOUR RESPONSES 1 AND 2.

9 Score RUBRIC FOR GEOMETRY OPEN-RESPONSE ITEM A (T.2.G.4, T.2.G.5B) Description 4 The student earns 4 points. The responses contain no incorrect work. The unit "feet" must be included in Parts 1 and 2. 3 The student earns 3 points. 2 The student earns 2 points. 1 The student earns 1 point. Some minimal understanding is shown. 0 The student earns 0 points. No understanding is shown. B Blank. No response. No attempt to answer the item.

10 Solution and Scoring Part 1: 2 points possible 1 point: Correct answer: 681 ft. AND 1 point: Correct and complete procedures shown or explained. Work may include a copy or calculation error, but not a procedural error = x 2 x 2 = Part 2: 2 points possible x = ft. The sterns of the ship would have been about 681 feet apart if the ships would have collided at their bows. 1 point: Correct answer: 269 ft. AND 1 point: Correct and complete procedures shown or explained. Work may contain a calculation or copy error, but not a procedural error. Give credit for the following or equivalent. 380 = 2 x sin 45 o = x 380 x 2 + x 2 = = x x = ft. OR = x 380 x = ft. OR 2x 2 = 144,400 x 2 = 72,200 x = ft. The stern of the Titanic would have been about 269 feet above the water at this time.

11 STAR CITY Math / Geometry / Special Right Triangles Answer Key and Alignment Answer Source SLE 1. B TLI T.2.G.4 2. A TLI T.2.G.5a 3. B TLI T.2.G.5b 4. B TLI T.2.G.5a 5. B TLI T.2.G.4 6. C AR T.2.G.5a 7. C TLI T.2.G.5b 8. C TLI T.2.G.4 9. B AR T.2.G.5b 10. B TLI T.2.G.5a 11. D AR T.2.G.5b 12. B TLI T.2.G B TLI T.2.G.5b 14. B AR T.2.G.5a

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