Geometry Final Ch 8

A steel cable supports an electrical tower as shown. The cable makes a 65* angle with the ground. The base of the cable is 17 ft from the tower. What is the height of the tower to the nearest foot? F) 8 feet G) 15 feet H) 36 feet J) 40 feet

H 36 feet p532 #69

Find the geometric mean of each pair of numbers. If necessary, give the answer in the simplest radical form. 3 and 15

3 sq root 5 p521 #19

Find the geometric mean of each pair of numbers. If necessary, give the answer in the simplest radical form. 2/3 and 27/40

3 sq root 5/10 p521 #23

Find each length. Round to the nearest 100th. PQ

3.58 CM p530 #37

Find each measure. Round lengths to the nearest 10th and angle measures to the nearest degree. m angle Z

33* p556 #33

Use your calculator to find each angle measure to the nearest degree. cos -1(5/6)

34* p537 #9

Find the indicated measure in each rectangle. Round to the nearest degree. m angle STV

35* p539 #55

Use your calculator to find each angle measure to the nearest degree. cos -1(0.8)

37* p538 #29

Use your calculator to find each angle measure to the nearest degree. sin -1(0.61)

38* p537 #11

Give each answer in simplest radical form. AC = 16, and CD = 5. Find BC.

4 square root 5 p522 #37

Write each trigonometric ratio as a fraction and as a decimal rounded to the nearest 100th. Tan C

4/3 ~ 1.33 p529 #7

Write each trigonometric ratio as a fraction and as a decimal rounded to the nearest 100th. Sin C

4/5 = .80 p529 #3

Write each trigonometric ratio as a fraction and as a decimal rounded to the nearest 100th. Cos A

4/5 = .80 p529 #5

The ambiguous case of the Law of Sines occurs when you are given an acute angle measure and when the side opposite this angle is shorter that the other given side. In this case, there are tow possible triangles. Find two possible values for m angle C to the nearest degree. (Hint: the inverse sine function on you calculator gives you only acute angle measures. Consider this angle and its supplement.)

42*, 138* p556 #49

Find each measure. Round lengths to the nearest 10th and angle measures to the nearest degree. m angle B

43* p555 #11

Find each measure. Round lengths to the nearest 10th and angle measures to the nearest degree. m angle Q

44* p555 #13

Find each length. Round to the nearest 100th. KL

5.27 ft p530 #41

Use figure to solve. Round lengths to the nearest 10th and angle measures to the nearest degree. a = 2.2m, b = 3.1m, and c = 4m. Find m angle B.

50* p556 #41

Use your calculator to find each trigonometric ratio. Round to the nearest 100th. cos 88*

0.03 p529 #15

Use your calculator to find each trigonometric ratio. Round to the nearest 100th. tan 9*

0.16 p529 #17

Use your calculator to find each trigonometric ratio. Round to the nearest 100th. cos 77*

0.22 p529 #33

Use your calculator to find each trigonometric ratio. Round to the nearest 100th. sin 23*

0.39 p529 #13

Use a calculator to find each trigonometric ratio. Round to the nearest 100th. sin 147*

0.54 p555 #7

Find the sine of the smaller acute angle in a triangle with side lengths of 3, 4, and 5 inches.

0.6 p531 #53

Use a calculator to find each trigonometric ratio. Round to the nearest 100th. sin 128*

0.79 p555 #25

Use your calculator to find each trigonometric ratio. Round to the nearest 100th. sin 55*

0.82 p529 #35

Complete each statement. If necessary, round angel measures to the nearest degree. Round other values to the nearest 100th. sin -1( ? ) ~ 69*

0.93 p538 #43

Use a calculator to find each trigonometric ratio. Round to the nearest 100th. sin 98*

0.99 p555 #21

Find the indicated length in each rectangle. Round to the nearest 10th. BC

1.2 ft p530 #49

Use your calculator to find each trigonometric ratio. Round to the nearest 100th. tan 51*

1.23 p529 #31

Use a special right angle to write each trigonometric ratio as a fraction. sin 30*

1/2 p529 #29

Use a special right angle to write each trigonometric ratio as a fraction. Cos 60*

1/2 p529 #9

Find the geometric mean of each pair of numbers. If necessary, give the answer in the simplest radical form. 2 and 50

10 p521 #5

Find each measure. Round lengths to the nearest 10th and angle measures to the nearest degree. EF

10.4 p555 #29

The geometric mean of two numbers is 2 square root 5. One of the numbers is 6. Find the other number.

10/3 or 3 1/3 p522 #29

Find x, y, and z

12;4 sq root 13;8 p521 #13

Write each trigonometric ratio as a fraction and as a decimal rounded to the nearest 100th. cos F

15/17 ~ 0.88 p529 #25

Write each trigonometric ratio as a fraction and as a decimal rounded to the nearest 100th. sin D

15/17 ~ 0.88 p529 #27

Write each trigonometric ratio as a fraction and as a decimal rounded to the nearest 100th. tan D

15/8 ~ 1.88 p529 #23

To estimate the height of Taipei 101 tower, Andrew stands so that his lines of sight to the top and bottom of the tower form a 90 degree angle. What is the height of the tower to the nearest foot?

1670 ft p522 #27

Find each measure. Round lengths to the nearest 10th and angle measures to the nearest degree. AB

17.3 p555 #15

When the angle of elevation to the sun is 37*, a flagpole casts a shadow that is 24.2 ft long. What is the height of the flagpole to the nearest foot?

18 ft p547 #7

Use your calculator to find each angle measure to the nearest degree. sin -1(0.31)

18* p538 #27

Find the perimeter and area of each triangle. Round to the nearest 100th.

18.64 cm 16.00 cm2 p531 #63

Find each length. Round to the nearest 100th. GH

19.67 ft p530 #39

A forest ranger in a 120 ft observation tower sees a fire. The angle of depression to the fire is 3.5*. What is the horizontal distance between the tower and the fire? Round to the nearest foot.

192 ft p548 #15

Find the geometric mean of each pair of numbers. If necessary, give the answer in the simplest radical form. 1/2 and 8

2 p.521 #7

Find x, y, and z

2 sq root 15;2 sq root 6;2 sq root 10 p521 #11

Find the geometric mean of each pair of numbers. If necessary, give the answer in the simplest radical form. 1/4 and 80

2 sq root 5 p521 #21

Find the geometric mean of each pair of numbers. If necessary, give the answer in the simplest radical form. 16 and 25

20 p521 #9

Find x, y, and z

20 sq root 3;10 sq root 21;20 sq root 7 p521 #25

Find each measure. Round lengths to the nearest 10th and angle measures to the nearest degree. PR

20.6 p555 #27

Find each measure. Round lengths to the nearest 10th and angle measures to the nearest degree. m angle G

21* p556 #37

Find the perimeter and area of each triangle. Round to the nearest 100th.

22.60 in 14.69 in2 p531 #65

The side lengths of a right triangle are given below. Find the measures of the acute angles in the triangle. Round to the nearest degree. 5, 12, 13

23*, 67* p539 #49

Use your calculator to find each angle measure to the nearest degree. tan -1(1.55)

57* p538 #31

A jump ramp for the waterskiing make a angle of 15* with the surface of the water. The ramp rises 1.58 m above the surface. What is the length of the ramp to the nearest 100th of a meter? the cosine of a 30* angle is equal to the sine of a ? angle.

60* p530 #47

Find the indicated measure in each rhombus. Round to the nearest degree. m angle LKN

62* p539 #57

The map of a beginning orienteering course is shown. To nearest degree, at what angle should a team turn in order to go from the first checkpoint to the second checkpoint?

63* p556 #45

From the top of a canyon, the angle of depression to the far side of the river is 58*, and the angle of depression to the near side of the river is 74*. The depth of the canyon is 191 m. What is the width of the river at the bottom of the canyon? Round to the nearest 10th of a meter.

64.6 m p547 #9

Use your calculator to find each angle measure to the nearest degree. tan -1(2.1)

65* p537 #7

Find each measure. Round lengths to the nearest 10th and angle measures to the nearest degree. m angle X

65* p555 #31

Architecture. a pediment has a pitch of 15*, as shown. If the width of the pediment, WZ, is 56ft, what is XY to the nearest inch?

7 '6" p529 #21

Complete each statement. If necessary, round angel measures to the nearest degree. Round other values to the nearest 100th. tan ? ~ 3.5

74* p538 #39

Use figure to solve. Round lengths to the nearest 10th and angle measures to the nearest degree. m angle A = 74*, m angle B = 22*, and b=3.2 cm. Find a.

8.2 cm p556 #39

Find each measure. Round lengths to the nearest 10th and angle measures to the nearest degree. EF

8.4 p556 #35

Find each length. Round to the nearest 100th. QR

965 M p529 #19

Which expression represents the length of RS? A) \(y+1) B) \y C) y2 D) y(y+1)

A p523 #49

To the nearest degree, what is the measure of the acute angle formed by Jefferson St. and Madison St.? A) 27* B) 31* C) 59* D) 63*

A p540 #67

Which of these is closest to the length of line AB? A) 5.5 cm B) 7.5 cm C) 14.4 cm D) 22.2 cm

A 5.5 cm p558 #59

A surveyor finds that the face of a pyramid makes a 135* angle with the ground. From a point 100m from the base of the pyramid, the angle of elevation to the top is 25*. How long is the face of the pyramid , line XY? A)48 m B) 81 m C) 124 m D) 207 m

C 124 m p558 #61

Lee is building a skateboard ramp based on the plan shown. Which is closest to the length of the ramp from point X to point Y? A) 4.9 ft B) 5.7 ft C) 8.5 ft D) 9.4 ft

D p523 #47

Which expression can be used to find m angle A? A) (tan)-1 (0.75) B) (sin)-1 (3/5) C) (cos)-1 (0.8) D) (tan)-1 (4/3)

D p540 #65

True or false. If false, tell why. as you watch a plane fly above you, the angle of elevation to the plane gets closer to 0* and the plane approaches the point directly overhead.

F p548 #19

Write a similarity statement comparing the three triangles in the diagram

^ BED~ ^ECD ~ ^ BCE p.521 #3

Write a similarity statement comparing the three triangles in the diagram

^MPN ~^PQN ~^MQP p521 #15

Write a similarity statement comparing the three triangles in the diagram

^RSU ~ ^RTS ~ ^STU p521 #17

Use the diagram to complete each equation.

z p522 #33

Verify that (sin A)2 + (cos A)2 = 1 for each angle measure. M angle A = 30*

(1/2)2 + (square root 3/2)2 p531 #59

Use a calculator to find each trigonometric ratio. Round to the nearest 100th. cos 95*

-0.09 p555 #17

Use a calculator to find each trigonometric ratio. Round to the nearest 100th. cos 133*

-0.68 p555 #5

Use a calculator to find each trigonometric ratio. Round to the nearest 100th. tan 139*

-0.87 p555 #23

Use a calculator to find each trigonometric ratio. Round to the nearest 100th. cos 156*

-0.91 p555 #9

Use a calculator to find each trigonometric ratio. Round to the nearest 100th. tan 118*

-1.88 p555 #19

Use a calculator to find each trigonometric ratio. Round to the nearest 100th. tan 92*

-28.64 p555 #3

For each triangle, find the side lengths to the nearest 100th and the angle measures to the nearest degree. A(-1,1), B(1,1), C(1,5)

AB = 2; BC = 4; AC ~ 4.47; m angle B =90*; m angle A ~ 63*; m angle C ~ 27* p537 #19

Classify each angle as an angle of elevation or angle of depression. angle 4

Angle of depression p547 #13

Classify each angle as an angle of elevation or angle of depression. angle 2

Angle of elevation p547 #11

Classify each angle as an angle of elevation or angle of depression. angle 1

Angle of elevation p547 #3

Classify each angle as an angle of elevation or angle of depression. angle 3

Angle of elevation p547 #5

Jessika is creating a pattern for a piece of stained glass. Find BC, AB and m angle ABC. Round lengths to the nearest 100th and angle measures to the nearest degree.

BC ~ 10.73; AB ~ 10.34; m angle ABC ~ 50* p557 #55

Jeff finds that a office building casts a shadow that is 93 ft long when the angle of elevation to the sun is 60*. What is the height of the building? F) 54 feet G)81 feet H) 107 feet J) 161 feet

J 161 ft p549 #29

Find the unknown measures. Round lengths to the nearest 100th and angle measures to the nearest degree.

JK ~ 2.88; LK ~ 1.40; m angle L = 64* p538 #33

Apply the vocabulary from this lesson to answer each question. In ^JKL, angle K if right angle. Write the sine of angle J as a ratio of side lengths.

LK/JL p529 #1

Identify whether you would use the Law of Sines or Law of Cosines as the first step when solving the given triangle.

Law of Sines p557 #51

Identify whether you would use the Law of Sines or Law of Cosines as the first step when solving the given triangle.

Law of Sines p557 #53

For each triangle, find the side lengths to the nearest 100th and the angle measures to the nearest degree. M(3,2), N(3,-2), P(-1,-2)

MN = NP = 4; MP ~ 5.66; m angle N = 90*; m angle M = m angle P = 45* p538 #37

Find the unknown measures. Round lengths to the nearest 100th and angle measures to the nearest degree.

QR ~ 4.90; m angle P ~ 36*; m angle R ~ 54* p538 #35

Find the unknown measures. Round lengths to the nearest 100th and angle measures to the nearest degree.

RP ~ 9.42; m angle P ~ 19*; m angle R ~ 71* p537 #13

For each triangle, find the side lengths to the nearest 100th and the angle measures to the nearest degree. R(3,3), S(-2,3), T(-2,-3)

RS = 5; ST = 6; RT ~ 7.81; m angle S = 90*; m angle R ~ 50*; Mm angle T ~ 40* p537 #17

True or false. If false, tell why. The angle of elevation from your eye to the top of a tree increases as you walk toward a tree.

T p548 #17

Find the unknown measures. Round lengths to the nearest 100th and angle measures to the nearest degree.

YZ ~ 13.96; m angle Y ~ 38*; m angle Z ~ 52* p537 #15

A surveyor finds that the angle of elevation tot he top of a 1000 ft tower is 67*. a. To the nearest foot, how far is the surveyor from the base of the tower? b. How far back would the surveyor have to move so that the angle of elevation to the top of the tower is 55? Round to the nearest foot.

a. 424 ft b. 276 ft p548 #25

The coordinates of the vertices of a triangle are A(-1,0), B(6,1), and C(0,3). a. Use the Distance Formula to find AB, BC, and AC. b. Use the Converse of the Pythagorean Theorem to show that ^ ABC is a right Triangle. Identify the right angle. c. Find the measures of the acute angles of ^ ABC. Round to the nearest degree.

a. AB = 5 square root 2; BC = 2 square root 10; AC square root 10. b. AC2 + BC2 = AB2, so ^ABC is a rt triangle and angle C is the rt angle. c. m angle A = 63*; m angle B =27* p539 #53

The equation (sin A)2 = (cos A)2 = 1 is known as a Pythagorean Identity. a. Write sin A and cos A in terms of a, b, and c. b. Use your results from part (a) to prove the identity (sin A)2 + (cos A)2 = 1.

a. sin A = a/c; cos A = b/c b. (sin A)2 + (cos A)2 = (a/c)2 + (b/c)2 = a2/c2 + b2/c2 =a2 + b2 / c2 =c2/c2 = 1. p531 #61

Use the given trigonometric ratio to determine which angle of the triangle is angle A. sin A = 4/5

angle 1 p537 #1

Use the given trigonometric ratio to determine which angle of the triangle is angle A. cos A = 0.6

angle 1 p537 #3

Use the given trigonometric ratio to determine which angle of the triangle is angle A. sin A = 12/13

angle 1 p538 #23

Use the given trigonometric ratio to determine which angle of the triangle is angle A. tan A = 0.75

angle 2 p537 #5

Use the given trigonometric ratio to determine which angle of the triangle is angle A. tan A = 5/12

angle 2 p538 #21

Use the given trigonometric ratio to determine which angle of the triangle is angle A. cos A = 12/13

angle 2 p538 #25

Which angles are not angle of elevation or angles of depression?

angles 1 and 3 p548 #21

Complete each statement. If necessary, round angel measures to the nearest degree. Round other values to the nearest 100th. ? 42* ~ 0.74

cos p538 #41

A jump ramp for the waterskiing make a angle of 15* with the surface of the water. The ramp rises 1.58 m above the surface. What is the length of the ramp to the nearest 100th of a meter? For a 45* angle, the ? and ? ratios are equal.

sine, cosine p530 #45

Give each answer in simplest radical form. BC = square root 5. and AC = square root 10. Find CD.

square root 10 / 2 p522 #39

Use a special right angle to write each trigonometric ratio as a fraction. Sin 45*

square root 2 /2 p529 #11

Use the diagram to complete each equation.

x p522 #35

Use the diagram to complete each equation.

x + y p522 #31