Standardized Test Practice - Cumulative, Chapters What is the value of x in the figure below?
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1 1. What is the value of x in the figure below? 2. A baseball diamond is a square with 90-ft sides. What is the length from 3rd base to 1st base? Round to the nearest tenth. A 22.5 B 23 C 23.5 D 24 Use the Pythagorean theorem to find the value of x. The correct choice is A. A F ft G ft H ft J ft Use the Pythagorean theorem to find the length from 3 rd base to 1 st base. Let d be the length from 3 rd base to 1 st base. Therefore, the correct choice is H. H 3. The scale of a map is 1 inch = 4.5 kilometers. What is the distance between two cities that are 2.4 inches apart on the map? A 10.8 kilometers B 11.1 kilometers C 11.4 kilometers D 11.5 kilometers 1 inch = 4.5 kilometers So, 2.4 inches will be equal to (2.4)(4.5) or 10.8 kilometers. Therefore, the correct choice is A. A esolutions Manual - Powered by Cognero Page 1
2 4. What is the value of x in the figure below? Round to the nearest tenth. F 10.5 G 11.1 H 13.6 J 14.2 Use the cosine ratio to find the value of x. 6. Grant is flying a kite on the end of a string that is 350 feet long. The angle elevation from Grant to the kite is 74º. How high above the ground is the kite? Round your answer to the nearest tenth if necessary. F 336.4ft G ft H ft J 96.5 ft Therefore, the correct choice is G. G Use the sine ratio to find the value of y. The kite is ft above the ground. Therefore, the correct choice is F. F esolutions Manual - Powered by Cognero Page 2
3 7. GRIDDED RESPONSE Find x in the figure below. Round your answer to the nearest tenth if necessary. The component form for the wind s vector is. Use the Law of Cosines to find the value of x. Add the vectors for Amy and the wind. Now determine the vector's magnitude by using Pythagorean theorem. Let v be the velocity of Amy. The velocity is about 12.3 feet per second Amy is paddling her canoe across a lake at a speed of 10 feet per second headed due north. The wind is blowing 40º east of north with a velocity of 2.8 feet. What is Amy s resultant velocity? Express your answer as a vector. Show your work. Write the direction vector for Amy in component form. Due north is equivalent to 90 from the horizontal. Now find the vector's direction. Let a be the angle made by Amy with the horizontal with the horizontal is equivalent to 8.4 east of north. The resultant velocity is about 12.3 feet per second at a heading of 8.4 east of north, The component form for Amy s vector is. about 12.3 feet per second at a heading of 8.4 east of north, Write the direction vector for wind in component form. 40 east of north is equivalent to 50 from the horizontal. esolutions Manual - Powered by Cognero Page 3
4 9. Janice used a 16-inch dowel and a 21-inch dowel to build a kite as shown below. What is the perimeter her kite? 10. GRIDDED RESPONSE A model airplane takes off at an angle of elevation of 30º. How high will the plane be after traveling 100 feet horizontally? Round to the nearest tenth. Show your work. Let x be the height of the plane from the ground after traveling 100 ft horizontally. Use tangent ratio to find the value of x. Use the Pythagorean theorem to find the side length of the kite. Find the length of the smaller side. The diagonal divides the kite into two congruent Isosceles triangles. So, the other smaller side is also 10 in. The plane is 57.7 ft high after traveling 100 feet horizontally ft 15. Refer to the triangle shown below. The length of the longer side is 17 in. Therefore, the perimeter of the kite is 2( )in or 54 in. 54 in. a. Find x to the nearest tenth. b. Find y to the nearest tenth. c. Find z to the nearest tenth. Use the properties of similar triangles. Separate all three triangles and show them according to their similar sides. esolutions Manual - Powered by Cognero Page 4
5 Triangles with sides z, 12.5, x and y, x, 8 are similar. Triangles with sides y, x, 8 and 20.5, z, y are similar. Triangles with sides z, 12.5, x and 20.5, z, y are similar. a. 10 b c esolutions Manual - Powered by Cognero Page 5
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