GRIDDED RESPONSE

11. A roofer leans a 20-ft ladder against a house. The base of the ladder is 7 ft from the house. How high, in feet, on the house does the ladder reach? Round to the nearest tenth of a foot.

12. A ship's loading ramp is 15 ft long and makes an angle of 18 ° 18 degrees with the dock. How many feet above the dock, to the nearest tenth of a foot, is the ship's deck?

    

13. What is the value of x in the figure below?

    

14. The measure of an interior angle of a regular polygon is 135. How many sides does the polygon have?

15. A front view of a barn is shown. The doorway is a square. Using a scale of 1 in. : 7 ft, what is the height, in feet, of the barn's doorway?

    

16. In a 30 ° - 60 ° - 90 ° 30 degrees minus 60 degrees minus 90 degrees triangle, the longer leg measures 56 3  cm. 56 square root of 3 , cm. How many centimeters long is the hypotenuse?
17. The measure of an angle is 12 more than 5 times its complement. What is the measure of the angle?

Short Response

18. In the trapezoid below, B E = 2 x − 8 , D E = x − 4 ,  and  A C = x + 2 . b e , equals 2 , x , negative 8 comma d e equals x . negative 4 comma , and eh c equals , x plus 2 , .

    

    1. Write and solve an equation for x.
    2. Find the length of each diagonal.

19. Use the diagram below.

    

    1. Find the measures of ∠ C B D , ∠ C B A , angle c b d comma angle c b eh comma and ∠ B A C . angle b eh c .
    2. Find BC, AD, and AB to the nearest tenth.

Extended Response

20. A clothing store window designer is preparing a new window display. Using the lower left-hand corner of the window as the origin, she marks points at (1, 7), (4, 3), (9, 3), (12, 7), and (6.5, 11). The designer uses tape to connect the points to form a polygon. Is the polygon an equilateral pentagon? Justify your answer.

21. A youth organization is designing a 25 in.-by-40 in. rectangular flag, as shown below. The designers want the shaded triangles to be similar.

    

    1. What should DF be in order to make Δ E D F ~ Δ C B A ? cap delta e d f , tilde , cap delta c b eh , question mark Explain your reasoning.
    2. In square inches, how much dark fabric do the designers need? How much light fabric?
    3. Are the hypotenuses of the two triangles parallel? How do you know? (Hint: Use corresponding angles.)

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