Pérdida del derecho al cobro

Work through all the problems in this chapter review and check answers in the back of the book. Answers to all review problems are there, and following each answer is a number in italics indicating the section in which that type of problem is discussed. Where weaknesses show up, review appropriate sections in the text.

1.

2. An arc of the circumference of a circle subtends a cen-

tral angle of how many degrees?

3. Given two similar triangles, as shown in the figure, find a if c
20,000, a
4, and c
5.

1 8 2954
?

6. Which of the following triangles are similar? Explain why.

7. Is it possible in two triangles that are similar to have one with an obtuse angle and the other with no obtuse angle? Explain.

8. Explain why a triangle cannot have more than one obtuse angle. a b b c a c

4. Change 3620 to decimal degrees (to two decimal places). 5. Write a definition of an angle of degree measure 1.

Figure for 3 Figure for 6 120 120 21 21 39 39 (a) (b) (c)

A

22. Which of the following window displays from a graph-

ing calculator is the result of the calculator being set in degree mode and which is the result of the calculator be- ing set in radian mode?

23. Solve the right triangle in Problem 10, given

mm and mm. (Find angles to the nearest 0.1.)

24. Find the angles in Problem 23 to the nearest 10. 25. If an equilateral triangle has a side of 10 ft, what is its

altitude (to two significant digits)?

26. A curve of a railroad track follows an arc of a circle of

radius 1,500 ft. If the arc subtends a central angle of 36 how far will a train travel on this arc?

27. Find the area of a sector with central angle 36.5 in a

circle with radius 18.3 ft. Compute your answer to the nearest unit.

28. Solve the triangle in Problem 10, given

2343 and km.

29. Solve the triangle in Problem 10, given m and m. (Find angles to the nearest 0.01.)

30. Use a calculator to find csc 67.1357 to four decimal places.

31. Precalculus: Shadow Problem A person is standing 20 ft away from a lamppost. If the lamp is 18 ft above the ground and the person is 5 ft 6 in. tall, how long is the person’s shadow?

c
4,883 a
2,421 c
232.6 90 
a
15.7 b
13.3 9. If an office building casts a shadow of 40 ft at the same

time a vertical yardstick (36 in.) casts a shadow of 2.0 in., how tall is the building?

10. For the triangle shown here, identify each ratio:

(A) sin  (B) sec  (C) tan  (D) csc  (E) cos  (F) cot 

11. Solve the right triangle in Problem 10, given

cm and

12. Find the degree measure of a central angle subtended

by an arc of 8.00 cm in a circle with circumference 20.0 cm.

13. If the minute hand of a clock is 2.00 in. long, how far

does the tip of the hand travel in exactly 20 min? 14. One angle has a measure of 2714 and another angle

has a measure of 27.25. Which is larger? Explain how you obtained your answer.

15. Use a calculator to:

(A) Convert 674231 to decimal degree form. (B) Convert 129.317 to degree-minute-second form.

16. Perform the following calculations on a calculator and

write the results in DMS form: (A)

(B)

17. For the triangles in Problem 3, find b to two significant

digits if mm, mm, and mm.

18. For the triangle in Problem 10, identify by name each of

the following ratios relative to angle : (A) a/c (B) b/a (C) b/c (D) c/a (E) c/b (F) a/b

19. For a given value , explain why sin  is independent of the size of a right triangle having  as an acute angle.

20. Solve the right triangle in Problem 10, given

and m.

21. Find each  to the accuracy indicated.

(A) tan (to two decimal places) (B) 0.3721 (to the nearest 10)

(C) 
sin10.0559 (to the nearest second)


arccos
2.497 a
4.00  108 
6220 b
2.6  104 a
1.5  104 a
4.1  106 3(134718 952851) 821437  163245 
35.2. c
20.2 u 90  u a b c Figure for 10 Figure for 31

B

C

37. Precalculus: Balloon Flight Two tracking stations 525 m apart measure angles of elevation of a weather balloon to be 73.5 and 54.2, as indicated in the figure. How high is the balloon at the time of the measurements?

38. Navigation: Chasing the Sun Your flight is west- ward from Buffalo, NY, and you notice the sun just above the horizon. How fast would the plane have to fly to keep the sun in the same position? (The latitude of

32. Construction The front porch of a house is 4.25 ft high. The angle of elevation of a ramp from the ground to the porch is 10.0 (see the figure). How long is the ramp? How far is the end of the ramp from the porch?

35. Precalculus: Balloon Flight The angle of elevation from the ground to a hot air balloon at an altitude of 2,800 ft is 64. What will be the new angle of elevation if the balloon descends straight down 1,400 ft?

36. Surveying Use the information in the figure to find the length x of the island.

4.25 ft 10

33. Medicine: Stress Test Cardiologists give stress tests by having patients walk on a treadmill at various speeds and inclinations. The amount of inclination may be given as an angle or as a percentage (see the figure). Find the angle of inclination if the treadmill is set at a 4% incline. Find the percentage of inclination if the angle of inclination is 4. Figure for 32 Figure for 36 Figure for 37 Figure for 33 a a b b u Angle of inclination: u Percentage of inclination:

34. Geography/Navigation Find the distance (to the near- est mile) between Green Bay, WI, with latitude 4431N and Mobile, AL, with latitude 3042N. (Both cities have approximately the same longitude.) Use

mi for the earth’s radius.

r
3,960 Island Horizontal line Altitude
2,850 m 43 52 x Weather balloon Station A Station B ? 54.2 73.5 525 m

*

*

*

*

Buffalo is 4250N, the radius of the earth is 3,960 mi, and the earth makes a complete rotation about its axis in 24 hr.)

39. Solar Energy A truncated conical solar collector is aimed directly at the sun as shown in part (a) of the fig- ure. An analysis of the amount of solar energy absorbed by the collecting disk requires certain equations relating the quantities shown in part (b) of the figure. Find an equation that expresses

(A)  in terms of  (B) r in terms of  and h (C) in terms of r, R, and 

(Based on the article, “The Solar Concentrating Proper- ties of a Conical Reflector,” by Don Leake in The

UMAP Journal, Vol. 8, No. 4, 1987.) H h

Figure for 38

Figure for 40

Figure for 39

Latitude 4250 N

(A) How is the required length of the ladder affected as the foot of the ladder moves away from the fence? How is the length affected as the foot moves closer to the fence?

(B) Express the length of the ladder in terms of the dis- tance from the fence to the building, the height of the fence, and , the angle of elevation that the lad- der makes with the level ground.

(C) Complete the table, giving values of L to two deci- mal places:

Parallel solar rays

Truncated reflecting cone Collecting disk (a) (b) b b H h R a r 5 ft 4 ft  25 35 45 55 65 75 85 L 16.25

(D) Explain what happens to L as  moves from 25 to 85. What value of  produces the minimum value of L in the table? What is the minimum value? (E) Describe how you can continue the process to get a

better estimate of the minimum ladder length. 40. Precalculus: Optimization A 5 ft fence is 4 ft away

from a building. A ladder is to go from the ground, across the top of the fence to the building. (See the fig- ure.) We want to find the length of the shortest ladder that can accomplish this.

41. Surveying A triangular plot is marked by posts at A,

B, and C (see the figure). Using AB as a baseline, a sur-

veyor measures angle CAB. Then she measures the dis- tance from A to B and angle ABC. Find, to the nearest foot, the distance from A to C and the distance from B to C.

B C

200 ft

A 40° 25°

42. Surveying Find the area of the plot of land in the fig- ure to the nearest square foot.

300 ft

110° 100 ft