53. Astronomy The Polish astronomer Nicolaus Copernicus devised a method for determining the sizes of the orbits of planets farther from the sun than Earth. His method involved noting the number of days between the times that a planet was in the positions labeled A and B in the diagram. Using this time and the number of days in each planet's year, he calculated c and d.

    
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    1. For Mars, c = 55.2 c equals , 55.2 and d = 103.8 . d equals , 103.8 , . How far is Mars from the sun in astronomical units (AU)? One astronomical unit is defined as the average distance from Earth to the center of the sun, about 93 million miles.
    2. For Jupiter, c = 21.9 c equals , 21.9 and d = 100.8 . d equals , 100.8 , . How far is Jupiter from the sun in astronomical units?

Standardized Test Prep

SAT/ACT

54. Grove Street has a grade of 20%. That means that the street rises 20 ft for every 100 ft of horizontal distance. To the nearest tenth, at what angle does Grove Street rise?

    

    1. 11 . 3 ° 11 . 3 degrees
    2. 11 . 5 ° 11 . 5 degrees
    3. 78 . 5 ° 78 . 5 degrees
    4. 78 . 7 ° 78 . 7 degrees

55. Which of the following figures is NOT a parallelogram?

    6. square
    7. trapezoid
    8. rhombus
    9. rectangle

Short Response

56. In Δ A B C , A B > B C > A C . cap delta eh b c comma eh b greater than b c greater than eh c . One angle has a measure of 168. What are all the possible whole-number values for the measure of ∠ A ? angle eh question mark Explain.

Mixed Review

See Lesson 8-2.

57. The length of the hypotenuse of a 30 ° - 60 ° - 90 ° 30 degrees minus 60 degrees minus 90 degrees triangle is 8. What are the lengths of the legs?
58. A diagonal of a square is 10 units. Find the length of a side of the square. Express your answer in simplest radical form.

Get Ready! To prepare for Lesson 8-4, do Exercises 59–62.

See Lessons 3-2 and 6-4.

Use rectangle ABCD to complete each statement.

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59. ∠ 1 ≅ ? _ angle 1 approximately equal to , modified question mark with under bar below
60. ∠ 5 ≅ ? _ angle 5 approximately equal to , modified question mark with under bar below
61. ∠ 3 ≅ ? _ angle 3 approximately equal to , modified question mark with under bar below
62. m ∠ 1 + m ∠ 5 = ? _ m angle 1 plus m angle 5 equals , modified question mark with under bar below

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