C Challenge

34. Firefighting A firefighter on the ground sees fire break through a window near the top of the building. The angle of elevation to the windowsill is 28 ° . 28 degrees . The angle of elevation to the top of the building is 42 ° . 42 degrees . The firefighter is 75 ft from the building and her eyes are 5 ft above the ground. What roof-to-windowsill distance can she report by radio to firefighters on the roof?

    

35. Geography For locations in the United States, the relationship between the latitude l and the greatest angle of elevation a of the sun at noon on the first day of summer is a = 90 ° − l + 23 . 5 ° . eh equals , 90 degrees , minus , l plus , 23 . 5 degrees . Find the latitude of your town. Then determine the greatest angle of elevation of the sun for your town on the first day of summer.

Standardized Test Prep

SAT/ACT

36. A 107-ft-tall building casts a shadow of 90 ft. To the nearest whole degree, what is the angle of elevation of the sun?

    1. 33 ° 33 degrees
    2. 40 ° 40 degrees
    3. 50 ° 50 degrees
    4. 57 ° 57 degrees

37. Which assumption should you make to prove indirectly that the sum of the measures of the angles of a parallelogram is 360?

    6. The sum of the measures of the angles of a parallelogram is 360.
    7. The sum of the measures of the angles of a parallelogram is not 360.
    8. The sum of the measures of consecutive angles of a parallelogram is 180.
    9. The sum of the measures of the angles of a parallelogram is 180.

Extended Response

38. A parallelogram has four congruent sides.

    1. Name the types of parallelograms that have this property.
    2. What is the most precise name for the figure, based only on the given description? Explain.
    3. Draw a diagram to show the categorization of parallelograms.

Mixed Review

See Lesson 8-3.

Find the value of x. Round to the nearest tenth of a unit.

Get Ready! To prepare for Lesson 8-5, do Exercises 42–44.

See Lesson 1-7.

Find the distance between each pair of points.

42. ( 0 , 0 )  and  ( 8 , 2 ) open 0 comma 0 close , and , open 8 comma 2 close
43. ( − 15 , − 2 )  and  ( 0 , 0 ) open negative 15 comma negative 2 close , and , open 0 comma 0 close
44. ( − 2 , 12 )  and  ( 0 , 0 ) open negative 2 comma 12 close , and , open 0 comma 0 close

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