Show all work for full credit. Do NOT use trig to solve special right triangle problems (half credit).

Transcription

1 Chapter 8 Retake Review 1 The length of the hypotenuse of a triangle is 4. Find the perimeter. 2 What similarity statement can you write relating the three triangles in the diagram? 5 Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree. 6 Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. 3 A hot air balloon is one mile above sea level when it begins to climb at a constant angle of 4 for the next 50 ground miles. About how far above sea level to the nearest tenth of a mile is the hot air balloon after its climb? 4 Wayne used the diagram to compute the distance from Ferris, to Dunlap, to Butte. How much shorter, to the nearest mile, is the distance directly from Ferris to Butte than the distance Wayne found? Not drawn to scale 7 Find the value of x to the nearest degree. 8 A forest ranger spots a fire from a 21-foot tower. The angle of depression from the tower to the fire is 12. a. Draw a diagram to represent this situation. b. To the nearest foot, how far is the fire from the base of the tower? Show the steps you use to find the solution. 9 A triangle has side lengths of 28 in, 4 in, and 31 in. Classify it as acute, obtuse, or right. 1

2 ID: A 10 The figure is drawn on centimeter grid paper. Find the perimeter of the shaded figure to the nearest tenth. 16 After flying at an altitude of 600 meters, a hot air balloon starts to descend when its ground distance from the landing pad is 10 kilometers. What is the angle of depression to the nearest tenth of a degree for this part of the flight? 17 Find the value of x to the nearest degree. 11 Find the geometric mean of the pair of numbers. 100 and 9 12 If AB Ä CD, find x and the length of CD. 13 To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 44. To the nearest foot, what is the height of the pole? 14 A digital camera with a panoramic lens is described as having a view with an angle of elevation of 38. If the camera is on a 3-foot tripod aimed directly at a 124-foot-tall monument, how far to the nearest tenth of a foot from the monument should you place the tripod to see the entire monument in your photograph? 15 A triangle has side lengths of 14 cm, 48 cm, and 50 cm. Classify it as acute, obtuse, or right. 18 Find the angle of elevation (nearest whole degree) to the peak of a mountain for an observer who is 155 meters from the mountain if the observers s eye is 1.5 meters above the ground and the mountain is 350 meters tall. 19 An A-frame house is 40 feet high and 30 feet wide. Find the angle that the room makes with the floor. Round to the nearest degree. 20 Find x. 21 A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the entrance door? 2

3 ID: A 22 The length of a diagonal of a square is 24 2 millimeters. Find the perimeter of the square. 23 A highway makes an angle of 6 with the horizontal. This angle is maintained for a horizontal distance of 8 miles. a. Draw and label a diagram to represent this situation. b. To the nearest hundredth of a mile, how high does the highway rise in this 8-mile section? Show the steps you use to find the distance. 24 Find the value of x. Round to the nearest degree. 28 A 30-foot tree casts a 12-foot shadow. Find the angle of elevation of the sun to the nearest degree. 29 Find the length of the leg. If your answer is not an integer, leave it in simplest radical form. 25 Find the value of the variable. If your answer is not an integer, leave it in simplest radical form. 30 A conveyor belt carries supplies from the first floor to the second floor, which is 24 feet higher. The belt makes a 60 angle with the ground. 26 Find the value of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree. How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot. If the belt moves at 75 ft/min, how long, to the nearest tenth of a minute, does it take the supplies to move to the second floor? 27 A triangle has side lengths 10, 16, and 11. Is the triangle acute, obtuse, or right? Explain. 3

4 ID: A 31 Find the value of x. Round your answer to the nearest tenth. 35 Find the value of x. Round the length to the nearest tenth. 32 Due to a storm, a pilot flying at an altitude of 528 feet has to land. If he has a horizontal distance of 2000 feet to land, at what angle of depression (nearest tenth of a degree) should he land? 33 Find the value of x. Round to the nearest degree. 36 A piece of art is in the shape of an equilateral triangle with sides of 13 in. Find the area of the piece of art. Round your answer to the nearest tenth. 37 Find the value of x. Round your answer to the nearest tenth. 34 Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale. 38 A slide 4.1 meters long makes an angle of 35 with the ground. To the nearest tenth of a meter, how far above the ground is the top of the slide? 39 Claire and Marisa are both waiting to get a rebound during a basketball game. If the height of the basketball hoop is 10 feet, the angle of elevation between Claire and the goal is 35, and the angle of elevation between Marisa and the goal is 25, how far apart to the nearest tenth of a foot are they standing? 4

5 ID: A 40 Dante is standing at horizontal ground level with the base of the Empire State Building in New York City. The angle formed by the ground and the line segment from his position to the top of the building is The height of the Empire State Building is 1472 feet. Find his distance from the Empire State Building to the nearest foot. 41 Viola drives 170 meters up a hill that makes an angle of 6 with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered? 42 The area of a square garden is 242 m 2. How long is the diagonal? 43 Find the value of w, then x. Round lengths of segments to the nearest tenth. 46 Two horses are observed by a hang glider 80 meters above a meadow. The angles of depression are 10.4 and 8. How far apart, to the nearest tenth of a meter, are the horses? 47 Find x in ABC. 48 A traffic helicopter pilot 60 meters above the road spotted two antique cars. The angles of depression are 10.2 and 8.7. How far apart to the nearest tenth of a meter are the cars? 49 Find the value of x. Round to the nearest tenth. 44 Find the length of the hypotenuse. 50 Find x. 45 Find the value of x. Round to the nearest tenth. 51 Find the value of x. Round to the nearest tenth. 5

6 ID: A Chapter 8 Retake Review Answer Section JMK MLK JLM mi 4 10 mi 5 tan 1 10ˆ Á 14 ; 36 6 x = 30, y = sin 1 3 ˆ Á 58 ; 23 8 a. b. tan 12 = 21 Use the tangent ratio. x 21 x = Solve for x. tan 12 x 99 The fire is about 99 feet from the base of the tower. 9 obtuse ; 17.6 cm x = 5 6 3, CD = ft ; feet tan38 15 right 16 tan 1 0.6ˆ Á 10 or 600 ˆ tan 1 Á 10,000 ; tan 1 19ˆ Á 11 ; 60 1

7 ID: A 18 tan ˆ Á 155 ; tan 1 40ˆ Á 15 ; millimeters 23 a. b. tan 6 = x 8 Use the tangent ratio. x = 8(tan 6 ) Solve for x. x 0.84 The rise is about 0.84 miles. 24 cos 1 15ˆ Á 21 ; w =10(sin50); 7.7 x = sin 1 7.7ˆ Á 11 ; The triangle is obtuse. The longest side length is 16. Let c = 16. Because a 2 + b 2 < c 2, the triangle is obtuse. 28 tan 1 30ˆ Á 12 ; ft; 0.4 min 9 31 tan20 ; tan ˆ Á 2000 ; sin 1 8 ˆ Á 14 ;

8 ID: A ( sin10) ; m in ; 6.2 cm tan55 38 ( sin35)4.1; 2.4 m ft ft 41 ( cos 6)170; m m 43 w = 13.3, x = cos 28 ; m m 49 (sin20)18; sin35 ;