STAR CITY Math / Geometry / Review: Right Triangles 1. Firefighters use a 20 foot extension ladder to reach 16 feet up a building. How far from the building should they place the base of the ladder? Name Teacher Period Use the figure below to answer question 3. A. 4 ft. B. 12 ft. C. 25.6 ft. D. 36 ft. 2. Tyler lives 9 miles north of the school. Hannah lives 9 miles east of the school. What is the shortest distance between Tyler and Hannah s houses? A. 81 miles B. 18 miles C. 9 2 miles D. 3 2 miles 3. Using the figure shown above, what is the most accurate measurement of the distance from the top of the flagpole to the spot where Jack is standing? A. 25 1 2 feet B. 36 feet C. 320 feet D. 656 feet 4. A football field is 360 feet by 45 feet. About how long is the walk from one corner diagonally to the opposite corner? A. 28.5 feet B. 315.0 feet C. 357.2 feet D. 362.8 feet 1
5. Which of the following forms a Pythagorean triple? 7. Find the value of x and y. A. 3, 4, 6 B. 5, 12, 14 C. 8, 15, 18 D. 12, 16, 20 6. At a golf course, Jack, J, drove his ball from the tee, T, 180 yards straight towards the hole, H. His cousin, Gary, G, drove his ball 225 yards, but not towards the hole. Gary s ball is now 168.75 yards from the hole. The diagram below shows their current positions. 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 = 2 9 8. Jimmy mows lawns in the summer. He needs to build a ramp for loading and unloading his mower from his truck. Using the design below, what is the length of the ramp? A. 1 3 8 ft. What is the distance from Jack s current position to the hole? A. 101.25 yd. B. 135.00 yd. B. 3 1 6 ft. C. 4 3 4 ft. D. 5 1 2 ft. C. 213.75 yd. D. 281.25 yd. 2
9. 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? 11. Charlie has caught his kite in the top of a tree, as shown in the figure below. He knows that the length of the kite s string is 180 feet, and the angle the string makes with the ground is 30 degrees. How far up the tree is his kite? A. 90 ft A. 35 2 ft. B. 35 3 ft. C. 140 3 3 ft. D. 35 ft. 10. A scale model of an airplane wing is shown below. B. 90 2 ft C. 90 3 ft D. 180 ft 12. Guy wires are attached to the top of a telephone pole. The guy wire is 28 ft. long. Find the height of the telephone pole to the nearest tenth of a foot. In ΔIGW, IN WG. Which statement could be used to prove that IN is an altitude? A. INW ING B. WN NḠ C. WI IḠ A. 14.0 ft. B. 16.2 ft. C. 19.8 ft. D. 24.2 ft. D. WIN GIN 3
13. The Iran Darab is a crude oil tanker. The picture below shows the tanker being pulled by a tug boat. If the cable that connects the tugboat to the tanker is at a 60 angle and the connection point on the tanker is 32 m above the tugboat, how far is the tugboat from the tanker? Use the figure below to answer question 15. 15. A paper airplane is shown in the figure above with a wing length of 12 inches. What is the length of AR? A. 6 inches B. 6 2 inches A. 32 3 m B. 32 2 m C. 6 3 inches D. 8 3 inches C. 64 m D. 32 3 3 m Use the figure below to answer question 14. 14. What is the value of x? A. 3 cm B. 3 2 cm C. 3 3 cm D. 3 cm 4
Use the diagram below to answer question 16. 18. As shown in the diagram below, a standard baseball diamond has 4 right angles and is 90 feet on a side. What is the shortest distance from first base to third base (indicated by the dotted line)? 16. 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. 40.0 ft. B. 56.6 ft. C. 69.3 ft. D. 80.0 ft. 17. In an isosceles right triangle, the side opposite the right angle is always a multiple of what number? A. 90 feet B. 90 2 feet C. 90 3 feet D. 180 feet 19. The perimeter of the square below is 36. What is the length of the diagonal, x? A. 2 B. π C. 2 3 D. 3 A. 6 B. 9 C. 6 2 D. 9 2 5
Use the segments below to answer question 20. STAR CITY Math Geometry Review: Right Triangles 20. Which step is not used in constructing a rectangle? A. Construct a perpendicular line through point A. B. Construct a perpendicular line through point B. C. Label a point, C, on the perpendicular line through point A. D. Draw an arc through AB from point C. 6
STAR CITY Math / Geometry / Review: Right Triangles Answer Key and Alignment Answer Source SLE 1. B TLI T.2.G.4 2. C TLI T.2.G.4 3. A AR T.2.G.4 4. D TLI T.2.G.4 5. D TLI T.2.G.4 6. A TLI T.2.G.4 7. C TLI T.2.G.4 8. D TLI T.2.G.5a 9. B TLI T.2.G.5a 10. A TLI M.3.G.5a 11. A AR T.2.G.5a 12. A TLI T.2.G.5a 13. A TLI T.2.G.5a 14. A TLI T.2.G.5a 15. C TLI T.2.G.5a 16. B AR T.2.G.5b 17. A AR T.2.G.5b 18. B AR T.2.G.5b 19. D AR T.2.G.5b 20. D TLI M.3.G.5b