Geometry



Math 2 - UNIT 5 – HOMEWORK PACKET

Math 2 Unit 5 Homework: DAY 1 – Pythagorean Theorem

For problems 1 – 3, using the Pythagorean Theorem, find the value of x.

1. 2. 3.

For problems 4 – 8, solve the word problems using the Pythagorean Theorem.

4. Find the third side of a right triangle is the hypotenuse is 14 km and one side is 9 km.

5. A rectangle is 6 ft long and 11 ft wide. What is the length of the diagonal of the rectangle?

6. A ladder 25-ft long is placed so that its top reaches 24 ft up the side of the house. How far from the house is the bottom of the ladder?

7. A tower casts a shadow 40 m long. The distance from the top of the tower to the end of the shadow is 50 m. How high is the tower?

8. Marie and Kevin hiked 3 miles east and then 6 miles north. How far were they from their starting point?

For problems 9 – 16, determine if it is possible to form a triangle with the given sides. If so, tell whether the triangle is right, acute, obtuse.

9. 6, 8, 10 10. 4, 9, 11

11. 1, 2, 3 12. [pic]

13. 5, 5, 12 14. 7, 8, 16

15. 10, 11, 13 16. 9, 40, 41

Math 2 Unit 5 Homework: DAY 2 – 45-45-90 Triangles

[pic]

Using the rule above, find x and y in each picture. Leave your answers in simplified radical form.

1. 2.

3. 4.

5. 6.

Math 2 Unit 5 Homework: DAY 2 Continued – 30-60-90 Triangles

Opposite of 30 is a

Opposite of 60 is [pic]

Opposite of 90 is 2a

1. 2.

3. 4.

5. 6.

Math 2 Unit 5 Homework: DAY 3 – Trigonometric Ratios

First decide whether you are solving for a side of a triangle or an angle. Then solve for x.

Round all answers to nearest hundredth.

1. cos 23( = [pic] 2. sin 87( = [pic] 3. tan 52( = [pic]

4. sin ( = [pic] 5. cos ( = [pic] 6. tan p = [pic]

7. sin A = sin B =

cos A = cos B =

tan A = tan B =

m(A = m(B =

8. sin A = sin B =

cos A = cos B =

tan A = tan B =

m(A = m(B =

9. Use the diagram to find the indicated measurement. Round your answers to the nearest hundredth.

10. Solve the right triangle (i.e. find all missing sides and angles). Round answers to nearest hundredth. Make sure you label your answers (i.e. m(A = _____, MN = _____, etc.)

Math 2 Unit 5 Homework: DAY 4 – Trigonometric Ratios

1. Solve for x.

a. sin 15( = [pic] b. cos 63( = [pic] c. tan x( = [pic]

x = __________ x = __________ x = __________

d. tan 30( = [pic] e. sin x( = [pic] f. cos 35( = [pic]

x = __________ x = __________ x = __________

Write ratios for sides and find the measures of angles.

2. sin A = __________ sin B = __________

cos A = __________ cos A = __________

tan A = __________ tan B = __________

m( = __________ m(B = __________

3. sin A = __________ sin B = __________

cos A = __________ cos A = __________

tan A = __________ tan B = __________

m( = __________ m(B = __________

Solve for the angle or the side.

4. 5. 6. 7.

x = __________ x = __________ x = __________ x = __________

8. 9. 10. 11.

x = __________ x = __________ x = __________ x = __________

12. Two legs of a right triangle are 16 and 48. Find the other side and all the angles.

13. One leg of a right triangle is 14 while the hypotenuse is 38. Find the other side and all the angles.

14. A 30-foot ladder is propped against a building. The angle it forms with the ground measures 47(. How far up the side of the building does the ladder reach? (draw a picture)

15. A ramp was built by the loading dock of a building. The height of the loading dock platform is 7 feet. Determine the length of the ramp if it makes a 38( angle with the ground. (draw a picture)

Math 2 Unit 5 Homework: DAY 5 – Angle of elevation and depression

1. A building 275 ft tall casts a 160 ft shadow. Find the measure of the angle of elevation to the top of the building.

2. A 40 ft ladder is leaning against a building. The ladder forms a 70° angle with the ground. How far is the bottom of the ladder from the base of the building?

3. A woman wants to use a 10 foot ladder to get to a window 8 ft above the ground. At what angle to the ground does the ladder need to be set?

4. At a point 125 ft from the base of a tower, the angle of elevation to the top of the tower has a degree measure of 38°. How high is the tower?

5. A 172 ft tall tree casts a shadow on the ground. If the angle of elevation is 49°, find the distance from the top of the tree to the tip of the shadow.

6. A pilot flying over level ground at an altitude of 2400 ft sights a building. The angle of

depression from the pilot to the building measures 6°. Find the ground distance

between the building and the point directly below the pilot.

7. The angle of depression from the top of a lighthouse to a boat is 27°. If the direct

distance from the top of the lighthouse to the boat is 462 ft, find the distance from the

base of the lighthouse to the boat.

8. From the top of a tower, the angle of depression to a stake on the ground is 72°. The top

of the tower is 80 feet above the ground. How far from the distance between the top of

the tower and the stake?

9. A ski slope is 550 yards long with a vertical drop of 130 yards. Find the angle of

depression of the slope.

10. An airplane is flying at an altitude of 1000 m. A tree is located 3500 m from a point

directly below the plane. Find the angle of depression from the plane to the tree.

Math 2 Unit 5 Homework: DAY 7 – Test Review

1. Find the value of c in the diagram given a = 4 and b = 7.

2. In the diagram, BC = 3 and AB = 9. What is the length of AC?

3. If a 25 foot ladder is placed against a wall so that it reaches a height of 7 feet, how far away from the is the bottom of the ladder?

4. A 25 foot wire is attached to the top of a 15 foot pole. How far from the bottom of the pole is the wire anchored into the ground?

5. Given a rectangle with a length of 36 and width of 15, find the diagonal.

6. A square has a diagonal of length 12. What is the perimeter of the square?

For problems 7 – 10, the following sets of numbers indicate the lengths of the sides of a triangle. Determine whether the triangle acute, obtuse, right, or not a triangle.

7. 5, 6, 11 8. 32, 15, 24 9. [pic] 10. 8, 12, 14

11. What is the Pythagorean Theorem?

12. What is the longest side of a right triangle called?

13. When do you use inverse trig?

14. If a leg is 3 in. and the hypotenuse is 5 in., what is the length of the other leg?

15. Given FGH shown, find the following trigonometric ratios in simplest form.

Sin G = _____ Sin F = _____

Cos G = _____ Cos F = _____

Tan G = _____ Tan F = _____

For problems 16 – 24, solve for x.

16. 17. 18.

19. 20. 21.

22. 23. 24.

25. In the diagram, CT = 10. 26. In the diagram, AD = 9, DC = 8 and BC = 15.

What is the length of AB? Find AB.

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

28. To the nearest tenth of a foot, how tall is a building 100 feet away (d = 100) if the top of the building is sighted at a 20° angle (n = 20)?

29. If an object is dropped from the top of the leaning tower of Pisa, it will land about 13 feet from the base of the tower. The tower leans at an angle of approximately 86°. What is the length of the leaning tower of Pisa?

30. Suppose a tree casts a shadow of length 60 feet. If the distance from the top of the tree to the end of the shadow is 80 feet, what is the angle of elevation from the shadow to the top of the tree?

31. A bird sits on top of a lamppost 20 meters tall. The distance from the bird to the feet of an observer is 25 meters. Find the angle of depression from the bird to the feet of the observer.

For problems 32 – 37, use the rules of special right triangles to find the values of x and y.

32. 33.

34. 35.

36. 37.

Test Review Answers ~

1. [pic]8.06

2. [pic]8.49

3. 24 ft.

4. 20 ft.

5. 39

6. P [pic]33.94

7. not a triangle

8. obtuse

9. right

10. acute

11. a² + b² = c²

12. Hypotenuse

13. To find the angle measure

14. 4 in.

15. Sin G = [pic], Cos G = [pic], Tan G = [pic]

Sin F = [pic], Cos F = [pic], Tan F = [pic]

16. 19.17

17. 7.52

18. 12.44

19. 19.83

20. 25.56

21. 11.02

22. 36.03°

23. 45.57°

24. 30°

25. [pic]4.33

26. [pic]8.94

27. 60 units

28. 36.4 ft.

29. 186.36

30. 41.41°

31. 53.13°

32. x=15, y=[pic]

33. x=[pic], y=16

34. x=13, y=[pic]

35. x=12, y=12

36. x=8, y=[pic]

37. x=[pic], y=[pic]

-----------------------

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[pic]

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9

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[pic]

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[pic]

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a.

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c.

c.

b.

a.

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e.

d.

a

b

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A

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36

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60

48

24

x

53°

34°

x

15

x

4

62°

28°

x

12

71°

32

31°

17

x

x

x°

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8

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7

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