Geometry Chapter 7 Review Right Triangles Use this review to help prepare for the Chapter 7 Test. The answers are attached at the end of the document.

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1 Use this review to help prepare for the hapter 7 Test. The answers are attached at the end of the document. 1. Solve for a and b. 2. Find a, b, and h a h b 10 b a The tangent of is. 4. A is a right triangle. A =.. Find the altitude of an isosceles triangle with base 10 and congruent sides of length Find sin P, cos P, tan P P 7. For each set of numbers, determine whether the numbers represent the lengths of the sides of an acute triangle, a right triangle, an obtuse triangle, or no triangle. A. 6, 9, 12..2, 4.2,.2. 8, 2, 1 D., 4, 7 8. Which of the following cannot be the lengths of a triangle? 9 [A] [] [] [D] 2, 9, , 4, 8, 16, 8, 2,

2 9. For the triangle shown below, the Pythagorean Theorem states that [A] e f g [] e = f + g [] f g e [D] e f g lassify a triangle with sides 10, 10, and 18 as acute, obtuse, or right. 11. The shorter leg of a triangle is 9.7 inches long. Find the perimeter. 12. Which triangle below is NOT congruent to the others? [A] [] [] [D] In a triangle, the ratio of the length of the hypotenuse to the length of a side is. [A] 2:1 [] 1:1 [] 2 :1 [D] :1 14. In a triangle, the ratio of the length of the hypotenuse to the length of the shorter side is. [A] :1 [] 2 :1 [] 2:1 [D] 2: 1. To find the height of a tower, a surveyor positions a transit that is 2 m tall at a spot 0 m from the base of the tower. She measures the angle of elevation to the top of the tower to be 9. What is the height of the tower, to the nearest meter?

3 16. If EFGH is a rectangle, what is FH? 17. The city commission wants to construct a new street that connects Main Street and North oulevard as shown in the diagram below. The construction cost has been estimated at $110 per linear foot. Find the estimated cost for constructing the street. (1 mile = 280 ft) North lvd. (new street) 9 mi W mi Main St. S E 18. Find the area of this right triangle if b 8 and c 10. c a b 19. Find the value of, to the nearest whole number. (not drawn to scale) G I 1 H

4 20. Solve the right triangle: 0 and a 18; find, b, and c c a b 21. Find the value of and y y 22. Name Pythagorean Triples (no multiples). 2. A radio station is going to construct a 6-foot tower for a new antenna. The tower will be supported by three cables, each attached to the top of the tower and to points on the roof of the building that are 8 feet from the base of the tower. Find the total length of the three cables. Draw it. [A] 0 ft [] 40 ft [] 0 ft [D] 10 ft 24. hoose the sets that are possible side lengths of a right triangle. A. 1, 1, 2. 1, 1, 2., 4, 7 D., 4, 2. An antenna is atop the roof of a 100-foot building, 10 feet from the edge, as shown in the figure below. From a point 0 feet from the base of the building, the angle from ground level to the top of the antenna is 66. Find, the length of the antenna, to the nearest foot. 10 ft 66 0 ft

5 26. The length of the diagonal of a square is 22. What is the length of each side? 27. Find the value of and y. y What is the length of an altitude of an equilateral triangle with side lengths 8? 29. A boat in calm seas travels 1 km east and km north. Find the distance of the most direct trip. 0. If the side lengths of a triangle are 7, 6, and 9, the triangle. [A] is an acute triangle [] cannot be formed [] is a right triangle [D] is an obtuse triangle 1. Use a calculator to find the value of cos 41 to four decimal places. 2. Write the trigonometric ratios. A. cos. tan A. sin. Write cos A. 1 A 12 [A] [] [] [D] 12 1

6 4. Find tan S.. Liola drives 21 km up a hill that is at a grade of 1. What horizontal distance, to the nearest tenth of kilometer, has she covered? [A] 4.7 km [] 12.1 km [] 4.8 km [D] 20. km 6. A baseball diamond is a square of side length 90 feet. How far is the throw, to one decimal place, from home plate to second base? 7. Which set of lengths cannot form a right triangle? [A] 7 mm, 8 mm, 10 mm [] 6 mm, 8 mm, 10 mm [] mm, 4 mm, mm [D] 12 mm, 16 mm, 20 mm 8. A telephone pole breaks and falls as shown. To the nearest foot, what was the original height of the pole? [A] 19 ft [] 21 ft [] 20 ft [D] 18 ft 7 ft 10 ft

7 9. What is the length of the diagonal of a square with side lengths 7 2? 40. Find the value of and y y 41. Find the length of the altitude drawn to the hypotenuse If PQRS is a rhombus, but not a square, what do we know about the length PR? 4. Find the perimeter and area of Trapezoid AD. A 2 m 2 m D List the angle and sides 4. List the angle and sides of A from least to greatest of A from least to greatest 6 7 A 6 6 A 8

8 46. What are the possible lengths of a the third side, if two sides of a triangles have sides lengths of: A: and 1 : 24 and Which side lengths allow you to construct a triangle? [A] 2,, and 8 [] 6, 8, and 10 [] 4, 1, and 9 [D] 7, 2, and Two sides of a triangle have lengths 8 and 11. What are the possible lengths of the third side? 49. D - Find the Area of Square DE - Find the Area of Isosceles Trapezoid AEF - Find the length of AE E G H A F GH = 9 D = 6 2 A =

9 2 6 [1] a =, b = 6 6 [2] a = 8, b = 8, h = 4 [] 9 7 [4] 117 [] 6 or 2 14 [6] sin P = 7 24, cos P =, 2 2 tan P = 7 24 [7] A. obtuse. acute. right D. no [8] [D] [9] [D] [10] obtuse [11] ( ) in. [12] [] [1] [] =4.9 in. [14] [] [1] 2 m [16] 6 [17] $,979, [18] 24 [19] 12 [20] β = 60 b = 18 = 1.18 c = 6 [21] = 6, y = 12 [22] [2] 0 feet [24] and D [2] ft [26] 11 2 [27] =, y = 6 [28] 12 [29] 4.7 km [0] [A] [1] a a b [2] A... c b c [] [] 4 [4] 7 [] [D] [6] 127. ft [7] [A] [8] [A] [9] 14 [40] = 2 2, y = [41] 4 [42] 0 < PR < 10 and PR 0 or 2 [4] Perimeter = m Area = m 2 [44],, A; A, A, [4], A, ; A,, A [46] A. 10 < < < < 6 [47] [48] < < 19 [49] Square 6 Trapezoid 6 AE = 97 = 9.8