30. House Repair After heavy winds damaged a house, workers placed a 6-m brace against its side at a 45 ° 45 degrees angle. Then, at the same spot on the ground, they placed a second, longer brace to make a 30 ° 30 degrees angle with the side of the house.

    

    1. How long is the longer brace? Round to the nearest tenth of a meter.
    2. About how much higher does the longer brace reach than the shorter brace?
31. Open-Ended Write a real-life problem that you can solve using a 30 ° - 60 ° - 90 ° 30 degrees minus 60 degrees minus 90 degrees triangle with a 12-ft hypotenuse. Show your solution.

32. Constructions Construct a 30 ° - 60 ° - 90 ° 30 degrees minus 60 degrees minus 90 degrees triangle using a segment that is the given side.

    1. the shorter leg
    2. the hypotenuse
    3. the longer leg

C Challenge

33. Geometry in 3 Dimensions Find the length d, in simplest radical form, of the diagonal of a cube with edges of the given length.

    

    1. 1 unit
    2. 2 units
    3. s units

Standardized Test Prep

SAT/ACT

34. The longer leg of a 30 ° - 60 ° - 90 ° 30 degrees minus 60 degrees minus 90 degrees triangle is 6. What is the length of the hypotenuse?

    1. 2 3 2 square root of 3
    2. 3 2 3 square root of 2
    3. 4 3 4 square root of 3
    4. 12

35. Which triangle is NOT a right triangle?

    6. 
    7. 
    8. 
    9. 

36. Suppose p is false and q is true. Which statement is NOT true?

    1. p → q p rightwards arrow q
    2. ~ q ∨ ( p ∧ q ) tilde q or open p and q close
    3. p ∨ q p or q
    4. ( p ∨ q ) ∧ ~ p open p or q close and tilde p

Short Response

37. In right Δ A B C , ∠ C cap delta eh b c , comma angle c is the right angle and C D ¯ c d bar is the altitude drawn to the hypotenuse. If A D = 3 eh d equals 3 and D B = 9 , d b equals 9 comma what is AC? Show your work.

Mixed Review

See Lesson 8-1.

38. A right triangle has a 6-in. hypotenuse and a 5-in. leg. Find the length of the other leg in simplest radical form.
39. An isosceles triangle has 20-cm legs and a 16-cm base. Find the length of the altitude to the base in simplest radical form.

Get Ready! To prepare for Lesson 8-3, do Exercises 40–43.

See Lesson 7-1.

Algebra Solve each proportion.

40. x 3 = 4 7 x over 3 , equals , 4 sevenths
41. 6 11 = x 9 6 elevenths , equals , x over 9
42. 8 15 = 4 x 8 fifteenths , equals , 4 over x
43. 5 x = 7 12 5 over x , equals , 7 twelfths

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