Name: __________________________________________ Period: ___________
Geometry
Unit 5: Right Triangles and Trigonometry
Homework
5.1: Pythagorean Theorem
Find the value of each variable or missing side. Leave answers in simplest radical form AND as a decimal rounded to the
hundredths place.
1.
5.
9.
6.
2.
10.
11.
12.
13.
14.
7.
3.
a = 4, b= 8
a = 7, b = 10
a = 6, c = 12
a = 3, b = 7
8.
4.
The numbers represent the lengths of the sides of a triangle. Classify each triangle as acute, obtuse, or right.
15. 6, 9, 10
17. 20, 100, 110
19. 2, 5, 6
16. 18, 24, 30
18. 7, 24, 25
20. 13, 21, 24
21. The bottom of a ladder must be placed 3 feet from a wall. The ladder is 12 feet long. How far above the ground
does the ladder touch the wall?
22. How far from the base of the house do you need to place a 15-foot ladder so that it exactly reaches the top of a
12 - foot tall wall?
23. A suitcase measures 24 inches long and 18 inches high. What is the length from corner to corner?
5.2: Special Right Triangles
Find the value of the variable. Leave answers in simplest radical form.
1.
2.
3.
7.
10.
4.
5.
6.
8.
9.
11.
12.
5.3: Sine, Cosine, and Tangent
Write the ratios for sine, cosine, and tangent for angle P and Q.
1.
3.
4.
2.
Find the value of x. Round answers to the hundredths place.
5.
6.
7.
14.
21.
15.
8.
22.
16.
23.
9.
17.
24.
10.
18.
25.
11.
19.
26.
12.
20.
27.
13.
5.4: Angles of Elevations
Describe each numbered angle as it relates to the diagram.
1.
2.
Find the value of x. Round the lengths to the nearest hundredth.
3.
6.
7.
4.
8.
5.
9. A person is standing 40 ft from a flagpole and can see the top of the pole at a 35º angle of elevation. The
person’s eye level is 4 ft from the ground. What is the height of the flagpole?
10. An eagle perched 40 ft up in a tree looks down at a 35º angle and spots a vole. How far is the vole from the
eagle?
11. You stand 40 ft from a tree. The angle of elevation from your eyes (5 ft above the ground) to the top of the tree
is 47º. How tall is the tree?
12. An airplane is flying at an altitude of 10,000 ft. The airport at which it is scheduled to land is 50 mi away. Find the
average angle at which the airplane must descend for landing.
13. A lake measures 600 ft across. A lodge stands on one shore. From your point on the opposite shore, the angle of
elevation to the top of the lodge is 4º. How high above the lake does the lodge stand?
14. A library needs to build an access ramp for wheelchairs. The main entrance to the library is 8 ft above sidewalk
level. If the architect designs the slope of the ramp in such a way that the angle of elevation is 5º, how long must
the access ramp be?
5.5: Vectors
Describe each vector as an ordered pair. Round the answers to the nearest hundredth.
1.
2.
3.
Find the magnitude and direction of each vector. Round your answers to the nearest hundredth.
4.
5.
6.
Use compass directions to describe the direction of each vector.
7.
8.
9.
Write the resultant as an ordered pair and draw the resultant.
10.
Sketch a vector that has the given direction.
13. 30° west of north
11.
14. 40° south of west
12.
15. 25° east of north
5.6: Trigonometry and Area
Find the area of each triangle. Round your answers to the nearest tenth.
4.
1.
7.
5.
2.
3.
8.
6.
9.
Find the area of each polygon. Round your answers to the nearest hundredth.
10. an equilateral triangle with apothem 5.8 cm
17. a square with radius 9 cm
11. a square with radius 17 ft
18. a triangular dog pen with apothem 4 m
12. a regular hexagon with apothem 19 mm
19. a hexagonal swimming pool cover with radius 5 ft
13. a regular pentagon with radius 9 m
20. an octagonal floor of a gazebo with apothem 6 ft
14. a regular octagon with radius 20 in.
21. a square deck with radius 2 m
15. a regular hexagon with apothem 11 cm
22. a hexagonal patio with apothem 4 ft
16. a regular decagon with apothem 10 in.
Unit 5 Review
Find the value of each variable. Express in simplest radical form.
1.
2.
Write each ratio for ∆ABC.
7. sinA
8. cosA
9. tanA
3.
5.
4.
6.
10. sinB
11. cosB
12. tanB
Find all of the missing sides and angles to the nearest thousandth.
15.
13.
14.
16.
Given the lengths of the sides of a triangle, identify the triangle as acute, right, or obtuse.
17. 37, 12, 34
18. 5, 12, 13
19. 20, 21, 28
Sketch a vector with the given direction.
20. 30° east of south
Use the vectors
22. the magnitude of
23. the magnitude of
,
21. 40° north of east
, and
to find each of the following.
24.
25.
Find the area of each figure.
26. Regular decagon with radius 5ft
27. Regular pentagon with apothem 8 cm
28. Regular hexagon with apothem 6in
29. Regular quadrilateral with radius 2m
30. Triangle with sides 15cm, 19cm and the angle between them 45°
31. Triangle with sides 15ft, 13ft, and the angle between them 65°
32. Triangle with sides 12m, 12m, and the angle between them 78°
33. A fire ranger stands at an observation window 70 ft above the ground. She sees a fire in the distance. She takes
a reading of the angle of depression and finds it to be 24°. To the nearest tenth of a foot, how far away from the
base of the tower is the fire?
34. Raul is 75 ft from the world’s tallest totem pole in Alert Bay, Canada. It is 173 ft tall. If Raul’s eyes are 5 ft from
the ground, what is the angle of elevation for his line of sight to the top of the totem pole? Round to the nearest
tenth.