honors math 2 unit 6 homework packet sanderson high school ...€¦ · homework 2: special right...

Honors Math 2 Unit 6 Homework Packet Sanderson High School

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Homework 1: Pythagorean Theorem (and converse) & Classifying Triangles

Solve for x. LEAVE ANSWERS AS SIMPLIFIED RADICALS, NOT DECIMALS.

1. X=__________

2. X=__________

3. X=__________

4. X=__________

5. X=__________

6. X=__________

7. X=__________

8. X=__________

9. X=__________

10. X=__________

11. X=__________

12. X=__________

13. X=__________

14. X=__________


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15. Find the length of the diagonals of square with a perimeter of 56. __________

16. A rectangle has diagonals of 5 cm and its width is √3 cm. Find the length of the rectangle. __________

17. The area of a square is 81 square centimeters. First, find the length of a side. Then, find the length of the diagonal.

18. John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school?

For Problems 19 and 20, use the picture to the right.

19. If AB = 8 and AD = 6, then DB = ________. And if HD = 5, then HB = ________

20. If AB = 12 and AD = 8, then DB = ________. And if HD = 9, then HB = ________

For Problems 21-28, tell if the given triangle is acute, right, or obtuse.

21.

22.

23.

24.

25.

26.

27.

28.


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Homework 2: Special Right Triangles

Solve for the missing sides in each of the given triangles using the relationships for special right triangles. Leave all

answers as simplified radicals.

1.

2.

3.

x = ____________

y = ____________

x = ____________

y = ____________

x = ____________

y = ____________

4.

5.

6.

x = ____________

y = ____________

x = ____________

y = ____________

x = ____________

y = ____________

7.

8.

9.

x = ____________

y = ____________

x = ____________

y = ____________

x = ____________

y = ____________

x

y 15

45

12√2

45

y

x

x

4√2 y

26

y

60

x 30 x

y

60

x

y

28

60 x

y

x

y 18

45

12√6

45

y

x


4

Homework 2: Special Right Triangles (Continued)

Solve for the missing sides in each of the given triangles using the relationships for special right triangles. Leave all

answers in terms of radicals.

1.

2.

3.

x = ____________

y = ____________

x = ____________

y = ____________

x = ____________

y = ____________

4.

5.

6.

x = ____________

y = ____________

x = ____________

y = ____________

x = ____________

y = ____________

7. In a 30°- 60°- 90°triangle, the shorter leg is 6ft long. Find the length of the other two legs.

Longer Leg = __________

Hypotenuse = __________

45

x

y

18 x

30

9

y

45

x

y

45

x

y

20 x

30

12√6

y

45

x

y


5

8. The hypotenuse of an isosceles right triangle is 10 inches. Find the length of the isosceles right triangle.

Length of the Side = __________

9. An altitude of an equilateral triangle is 𝟏𝟎√𝟑 units. What is the perimeter of the equilateral triangle?

Perimeter = __________

10. Find the length of the diagonal of a square that has sides of length 30cm.

Side Length = __________

11. The perimeter of a square is 32 fee. Find the length of one of the diagonals.

Length of the diagonal = __________

12. The diagonal of a rectangle splits the rectangle into two 30 60 90 triangles. If the diagonal is 14 inches,

find the perimeter of the rectangle.

Perimeter = __________

13. Jeremy is going to show off his skateboarding ability to his Math 2 class. He has a skate board ramp that must

be set-up to rise from the ground 30°. If the height from the ground to the platform is 8ft, how far is the ramp

from the platform? How long is the ramp up to the top of the platform?

Distance from the platform = __________

Length of the ramp = __________


6

Homework 4: Quadratics Review

Solve each equation by factoring or Quadratic Formula. Show all work.


7

Homework 5: Trigonometric Ratios


8

Homework 6: Solve using Trigonometric Ratios

For each of the following, write the equation to find the missing value. Then rewrite the equation that

you will enter in your calculator. Round your final answer to the nearest tenth.

1.

x _______

y _______

2.

x _______

y _______

3.

x _______

y _______

4.

x _______

y _______

5.

x _______

y _______

6.

x _______

y _______

7.

x _______

y _______

mB=______

8.

x _______

y _______

mA=_______

9.

w _______

x _______

y _______

z _______

10.

h _______

x _______

y _______

11. How tall is the tree? 12. A man who is 6 feet tall is flying a kite. The

kite string is 75 feet long. If the angle that the

kite string makes with the line horizontal to the

ground is 35, how far above the ground is the

kite?

36

8x

y

y

x

4

8

5

x

y

50

10 x

y64

x

y

12

4

xy

70

7.2

62

31’

16x

y20

A C

B

37

x

y

9

A

C

B

40˚ 25˚

20

x y

z w

y

55˚ 110

˚

h x 10


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Homework 7: Solve using Trigonometric Ratios

1. A boy flying a kite lets out 300 feet of string which makes an angle of 38o with the

ground. Assuming that the string is straight, how high above the ground is the kite?

2. A ladder leaning against the wall makes an angle of 74o with the ground. If the foot of

the ladder is 6.5 feet from the wall, how high on the wall is the ladder?

3. A straight road to the top of a hill is 2500 feet long and makes an angle of 12o with the

horizontal. Find the height of the hill.

4. An airplane climbs at an angle of 11o with the ground. Find the ground distance it has

traveled when it has attained an altitude of 400 feet.

5. A wire attached to the top of a pole reaches a stake in the ground 20 feet from the foot

of the pole and makes an angle of 58o with the ground. Find the length of the wire.


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6. Henry is flying a kite. The kite string makes an angle of 43o with the ground. If Henry is

standing 100 feet from a point on the ground directly below the kite, find the length of

the kite string.

7. A 25 foot ladder leans against a building. The ladder’s base is 13.5 feet from the

building. Find the angle which the ladder makes with the ground.

8. In order to reach the top of a hill which is 250 feet high, one must travel 2000 feet

straight up a road which leads to the top. Find the number of degrees contained in the

angle which the road makes with the horizontal.

9. A ladder leans against a building. The top of the ladder reaches a point on the building

which is 18 feet above the ground. The foot of the ladder is 7 feet from the building.

Find the measure of the angle which the ladder makes with the level ground.

10. A ladder is mounted on a fire truck, six feet above the ground. If the maximum length of

the ladder is 120 feet and the maximum angle to which it can be raised is 75o, how high

up will it reach?


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Homework 8: Solving Right Triangles

Solve for all of the missing sides and angles of the following right triangles.

1.

x = _______________

y = _______________

z = _______________

2.

x = _______________

y = _______________

z = _______________

3.

x = _______________

y = _______________

z = _______________

4.

x = _______________

y = _______________

z = _______________

30°

y

x

15

z

48°

y

x

15

z

45°

x

15√6 y

z

z

62°

x

y

35


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5.

x = _______________

y = _______________

z = _______________

6.

x = _______________

y = _______________

z = _______________

7.

x = _______________

y = _______________

z = _______________

8.

x = _______________

y = _______________

z = _______________

30°

19√3

y

x

z

16°

z

x

22

y

9

x

9√2

y

z

30

z

40

x

y


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Homework 9: Angles of Elevation & Depression

1. A wire is attached to the top of a 75 foot tower and meets the ground at a 65o angle.

How long is the wire?

2. When the sun’s angle of elevation is 57o, a building casts a shadow 21 meters long. How

high is the building?

3. A kite is flying at an angle of elevation of about 40o. All 80 meters of string have been

let out. Ignoring the sag in the string, find the height of the kite.

4. A man stands at the top of a 105 foot lighthouse and sees a boat. The angle of

depression to sight the boat is 37o. Find the distance between the base of the

lighthouse and the boat.

5. An observer in an airplane at a height of 500 meters sees a car at an angle of depression

of 31o. If the plane is over a barn, how far is the car from the barn?

6. From a point 340 meters from the base of the Hoover Dam, the angle of elevation to the

top of the dam is 33o. Find the height of the dam to the nearest meter.


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7. The Pyramid of the Sun in the ancient Mexican city of Teotihuacan was unearthed from

1904-1910. From a point on the ground 300 feet from the center of its square base, the

angle of elevation to its top would have been 31o. What was the height of the pyramid?

Complete the following statements with always, sometimes, or never.

Explain your answer with complete sentences.

8. The tangent of an angle is _______________ less than 1.

9. The angle of elevation from your eye to the top of a twenty-foot flagpole

_____________________ gets smaller as you walk towards the flagpole.

10. Given the measure of an acute angle in a right triangle and the length of one of the

triangle’s legs, you can ________________ use trigonometry to find the length of the

hypotenuse.

11. The angle of depression from the top of a building to a car traveling towards the building

__________________ increases as the car travels closer.


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Homework 10: Angles of Elevation and Depression

1. From a point 80 m from the base of a tower, the angle of elevation to the top of the tower is 28°. How tall is the

tower?

2. A ladder that is 20 ft long is leaning against the side of a building. If the angle formed between the ladder and

the ground is 75°, how far is the bottom of the ladder from the base of the building?

3. When the sun is 62° above the horizon, a building casts a shadow 18 m long. How tall is the building?

4. The mad scientist Maniacal Mike has created a machine can launch boulders to crush buildings in Super Hero

City. Maniacal Mike’s target this time is a satellite dish on top of the 200 ft tall Do-Gooder Labs. If Maniacal

Mike sets u his machine 1 mile (5280 ft) away, what angle will h need to launch at the hit the satellite dish on

top of the laboratory?

5. A kite is flying at an angle of elevation of about 55°. Ignoring that sag in the string, find the height of the kite if

85m of string have been let out.

6. A guy wire is attached to the top of a tower to help keep it from falling down. The wire is anchored to the

ground 35 m away from the base of the tower. If the wire makes a 65° angle with the ground, how long is the

wire?


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7. The angle of depression from the top of a tower to a boulder on the ground is 38°. If the tower is 25 m high,

how far from the base of the tower is the boulder?

8. A Russian submarine has been spotted off the coast North Carolina. The US Navy sent out the Destroyer

Michigan to blow up the submarine. The submarine will only be able to travel 1500 meters before the Destroyer

will catch up to it. If the Destroyers Depth Charges can reach up to 500 meters underwater, at what angle must

the Russian submarine descend to not be destroyed?

9. An observer at the top of a building sees a car on the road below. The angle of depression to the car is 28°. If

the car is about 50 m from the base of the building when it is seen, how tall is the building?

10. A 15 m pole is leaning against a wall. The foot of the pole is 10 m from the wall. Find the angle that the pole

makes with the ground.

11. At 11 o’clock the 20 ft Sanderson flag pole casts a shadow that is 30 ft long. What is the angle of elevation of the

sun at 11 o’clock?

12. Captain Awesome is trying to shoot down an enemy fighter using his rocket launcher from 200 meters away. If

the enemy fighter is 180 meters in the air, what angle will Captain Awesome need to fire his rocket launcher to

bring down the enemy aircraft?


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Homework 11: Clinometer Activity

1. Can you find the height of the tree when you are not standing on a horizontal surface, or without

knowing your own height? Angles are measured 30 m away from the tree (this measurement is

perpendicular to the tree). Solve and show your calculations below.

12°

5°

2. Explain how the angle shown on the protractor of your clinometer is related to the angle of

inclination that the clinometer measures.

3. A tree farmer stood 10.0 m from the base of a tree.

She used a clinometer to sight the top of the three.

The angle shown on the protractor scale was 40o. The

tree farmer held the clinometer 1.6 m above the ground.

Determine the height of the tree to the nearest tenth

of a meter. The diagram is NOT drawn to scale.

4. Use the information in the diagram to calculate the

height of a totem pole observed with a drinking-straw

clinometer. Give the answer to the nearest meter. The

diagram is NOT drawn to scale.

honors math 2 unit 6 homework packet sanderson high school ...€¦ · homework 2: special right...

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