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Chapter 9 test 2 answers • 1. The HYPOTENUSE is the side opposite the right angle in a right triangle. • 2. In a right triangle, if x and y are the lengths of the legs and z is the length of the hypotenuse, then _x2 + y2 = z2__ (formula). • 3. In an isosceles right triangle, if the hypotenuse has length x, then each leg has length _x/√2___. • 4. In a 30-60-90 triangle, if the hypotenuse has length y, then the shorter leg has length __y/2___ and the longer leg has length __y√3/2___. 5. Determine whether ABC with vertices A(2, 4), B(10, 2), and C(7, 7) is scalene, isosceles, or equilateral. a 2 + b 2 = c2 A( 2, 4) A( 2, 4) C( 7, 7) B(10, 2) C( 7, 7) B(10, 2) 82 + 22 = c2 52 + 32 = c2 3 2 + 52 = c 2 64 + 4 = c2 25 + 9 = c2 9 + 25 = c2 68 = c2 34 = c2 34 = c2 √68 = c √34 = c √34 = c isosceles 6. A jet flies under another at midnight. The lower jet is traveling south at 300 km/hr at an altitude of 12,500 feet; the other is traveling east at 400 km/hr at an altitude of 15,500. If they continue on their current flight paths, without varying their altitude or speed, how far apart will they be in 3 hours? a2 + b2 = c2 (300 • 3)2 + (400 • 3)2 = c2 9002 + 12002 = c2 810000 + 1440000 = c2 2250000 = c2 1500 = c 1500 km apart 7.Find the area of an equilateral triangle with sides measuring 8 meters. bh 2 4 • 4√3 16√3 16√3 m2 or 27.71 m2 8 4√3 8 4 8 4 8. To the nearest foot, find the original height of a fallen flagpole that cracked and fell as if hinged, forming an angle of 45 with the ground where it hit. The tip of the pole hit the ground 12 feet from its base which is still standing upright. 12 feet Since this is an isosceles right triangle, the two legs (the ground and the remaining upright portion of the flag pole are both 12 feet and the hypotenuse is 12√2. 12 + 12√2 = original height of flagpole 45º 12 + 12 • 1.4 12 + 16.8 28.8 feet The original height of the 90º 45º Flagpole was 28.8 feet. 12 feet Chapter 10 test 1 answers 1.The EDGES of a prism are the line segments where the lateral faces intersect. 2.A SPHERE is the set of all points at a given distance from a given point. 3.The altitude of a pyramid is a PERPENDICULAR segment from the VERTEX to the plane of the base. 4.An object’s density is calculated by dividing the MASS of the object by its VOLUME. 5. A scoop of ice cream, shaped like a sphere with a diameter 6 cm, is placed in an ice cream cone with diameter 5 cm and height 10 cm. Is the cone big enough to hold all the ice cream if it melts? Explain. Sphere 4πr3 3 4 • 3.14 • 3 • 3 • 3 3 113.04 cm3 > Cone πr2H 3 3.14 • 3 • 3 • 10 3 94.2 cm3 When the ice cream melts, it will over runneth the cone. 6. Which container would hold more popcorn: a can cylinder with a diameter of 7 inches and a height of 7 inches or a cardboard box that measures 7 inches on each edge? Cylinder πr2H 3.14 • 3.5 • 3.5 • 7 269.225 in3 < Prism bhH 7•7•7 343 in3 The cardboard box can hold more popcorn. 7. What are the smallest measurements [B (b and h) and H] would a pyramid have to have to hold the same amount of sand as a cone with a base radius of 3 inches and a height of 8 inches? Pyramid Cone The bhH πr2H dimensions for 3 3 3 the pyramid 3.14 • 9 • 8 3.14 • 3 • 3 • 8 could be 3 3 B = 3.14 • 9 3 3 99.36 in 99.36 in and H = 8 8. p. 537 # 9 D = m/v 3088 g 10 • 10 • 1.6 cm3 3088 g 160 cm3 D = 19.3 g/cm3 The medallion is gold and Colonel Banderson is whom he says he is.