1) 3) 4) Geometry/Trig 2 Name Unit 7 Review Packet Date Block ...

Geometry/Trig 2 Unit 7 Review Packet

Name __________________________ Date _______________ Block ______

Problems with a (d) will have a decimal answer. Round these answers to the nearest hundredth. All other answers must be left in simplified radical form. 1)

2)  22

x

x

6

x = ______



(d)  = ______

11

9

x = ______

(d)  = ______

3) z

x

2 2

4

x = ______

y

y = ______ z = ______

4)

w

w = ______ y

z

2 3

30

x = ______

30

x

y = ______ z = ______

5)

5 x

4 3

 17

x = ______ (d)  = ______

Geometry/Trig 2 Unit 7 Review Packet y

6)

x+1

4 z

x = ______ y = ______

8

z = ______

7) x = ______ x

30

10

z

y = ______ 45

y

z = ______

8) ß

x

x

15

 16

x = ______ (d)  = ______ (d) ß = ______

9) z

y

x+2

x = ______ x

2x + 1

y = ______ z = ______

Geometry/Trig 2 Unit 7 Review Packet II. Directions: Complete each word problem. Leave answers in simplified radical form. 10) Find the geometric mean between 6 and 8.

11) 12 is the geometric mean between x and 16. Find x.

12) Can a triangle be constructed with side lengths 4, 5, and 8? If so, determine whether the triangle could be a right , acute or obtuse triangle.

13) Can a triangle be constructed with side lengths 5, 7, and 8? If so, determine whether the triangle could be a right , acute or obtuse triangle.

14) An isosceles triangle has side lengths 6, 6 and 10. Find the length of the altitude drawn to the base.

15) The diagonal of a square has a length of 12in. Find the perimeter of the square.

16) An equilateral triangle has a perimeter of 45 inches. Find the length of the altitude.

17) A rhombus has diagonals of lengths 10m and 24m. Find the perimeter of the rhombus.

Geometry/Trig 2 Unit 7 Review Packet Directions: Express each value as a fraction. Leave all answers in simplified radical form. 18)

19)

4

 8

2 6

 2 2

sec  =

csc  =

cot  =

cos  =

sin  =

tan  =

III. Directions: Complete each word problem. Round answers to the nearest hundredth, if necessary. 20)You and your team are building a runway that will head toward an existing 500-foot tower. For safety reasons, the plane must be at least 200 feet above the tower when it flies over.

a) If a jet takes off from the ground and ascends steadily at an angle of 31º, will it clear the tower that is 1000 feet from the point that the jet leaves the ground?

b) If not, how far must the point of take off be from the tower?

Geometry/Trig 2 Unit 7 Review Packet III. Directions: Complete each word problem. Round answers to the nearest hundredth. 21) You and a friend wave to each other from the top of two buildings. You are looking up at your friend at an angle of 18 angle of elevation. You are standing on a 763 foot building. The height of the building that your friend is on is 795 feet. What is the approximate distance between the two buildings?

22) A tree casts a shadow 81 feet long. The angle of elevation from the end of the shadow to the sun is 42. What is the height of the tree?

23) A kite is 38 feet above the ground. The child is holding the end of the kite string 4 feet above the ground. The kite string makes a rising angle (angle of elevation) of 42 from the line of sight. Assuming that the string is pulled tight, how much string is out?

24) You are in a lighthouse communicating with a ship offshore. You want to determine how far the ship is from the cliff that the lighthouse is on, given that the top of the lighthouse is 200 feet above sea level and the angle of depression is 20. How far away is the ship? If a person on the ship looks up at the top of the lighthouse, what is the angle of elevation?