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Document 1282021
Name:_____________________________________ Date:_______ Period:______ Review Sheet: Trig Applications Algebra 2 Honors Review Sheet: Trig Applications Law of Cosines Given the following measures in ΔDEF, find the length of the third side to the nearest tenth. 1. e = 7, f = 8, m<D = 30 2. d = 10, e = 8, m<F = 60 3. d = 4, e = 8, m<F = 120 4. d = 3, f = 10, m<E= 120 5. d = 4, e = 9, m<F = 110 6. d = 5, e = 8, m<F = 40 The lengths of the sides of ΔRST are given. Find the greatest angle, to the nearest degree. 7. r = 4, s = 5, t = 6 8. r = 10, s = 13, t = 5 9. r = 3, s = 4, t = 2 10. Find, to the nearest degree, the measure of the base angle of an isosceles triangle whose sides measure 14, 14, and 8 units. Area of a Triangle Find the area of ΔABC, rounded to three decimals. (remember the angle must be included) !
11. a = 8, b = 9, sin  = 12. a = b = 14, m<B = 75 13. b = 16, c = 18, m<A = 150 !
Find, to the nearest tenth, the area of parallelogram ABCD if sides, s1 and s2, and angle A have the following measures. 14. s1 = 18, s2 = 14, m<A = 60 15. s1 = 23, s2 = 31, m<A = 42 16. The area of a parallelogram is 622, and the lengths of its sides are 42 and 54. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram. 17. The area of a parallelogram is 728, and the lengths of its sides are 48 and 56. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram. Law of Sines Find the indicated measures for ΔABC. Round lengths to the nearest centimeter and angles to the nearest degree. 18. m<A = 45, m<B = 60, a = 8, b = ? 19. m<C = 75, m<A = 45, b = 9, a = ? 20. b = 13, a = 8, m<B = 22, m<A = ? 21. m<C = 95, m<A = 70, b = 3, a = ? 22. In ΔABC, the measurements of <A = 33°40' and <B = 53°20’ and BC = 17.4 cm. Find the length, in centimeters of AC. Ambiguous Case For each of the following, first determine the number of triangles that can be constructed with the given measures. Then find, if possible, the indicated measures to the nearest degree. 23. m<A = 140, b = 10, a = 3 24. m<A = 50, a = 13, b = 16 25. m<A = 58, b = 13, a = 17 Forces and Vectors 26. Two forces of 18 lb and 20 lb act on a body at an angle of 120. Find the magnitude of the resultant force to the nearest tenth. 27. Two forces of 130 kg and 90 kg act on an object. The angle between the two forces is 54°. What is the magnitude of the resultant force, to the nearest tenth? 28. Two forces of 2 N and 12 N act on an object. The angle between the two forces is 62°. What is the magnitude of the resultant force, to the nearest tenth. 29. Kevin got his car stuck in the mud. He needs help from two trucks to pull it out. One truck applies a force of 1250 pounds, and the other truck applies a force of 1575 pounds. The angle between the two applied forces is 68o. Find the magnitude of the resultant force, to the nearest tenth of a pound. 30. Two forces of 27 pounds and 32 pounds act on an object. The angle between the two forces is 70o. Find the magnitude of the resultant force, to the nearest tenth of a pound. Using this answer, find the measure of the angle formed between the resultant and the larger force, to the nearest degree. Review Questions: 31. Determine the nature of the roots for the following equations. (a) x2 – 4x + 6 = 0 (b) 2x2 + x + 8 = 0 (c) x2 + 6x = -­‐9 32. How many different ways can teams of five members be formed from a class of 26 students? 33. Sabrina has room for 8 out of 10 books on her shelf. How many different ways can she arrange them? 34. Peter has 40 different students that he can choose from to be on his basketball team. He needs 8 players. How many different teams can be formed? !
35. The probability of Tim winning a race is . Calculate the exact probability that Tim will win at least !
three out of his next four races. 36. The probability that Gabe will hit a home run is 58%. Calculate the probability, to the nearest tenth of a percent, that Gabe will hit at most 2 homeruns in the next four games. 37. If f(x) = 2x + 6, find f(4x – 1). 38. If g(x) = 2x2 – 3x + 2, find g(2b – 3). 39. Find the inverse of h(x) = x2 – 8. 40. Find the inverse of f(x) = 5x + 9 41. The sum of 3 + 2i and 7 – 8i lies in which quadrant? 42. A wheel has a radius of 14 inches. Find the distance, to the nearest tenth of an inch, that the wheel !!
will travel when it rotates through an angle of radians. !
Review Sheet: Trig Applications Answer Key
1.) 4.0
2.) 9.2
3.) 10.6
4.) 11.8
5.) 11.0
6.) 5.3
7.) 83°
8.) 116°
9.) 104°
10.) 17°
11.) 9
12.) 49
13.) 72
14.) 218.2
15.) 477.1
16.) 15.9o
17.) 15.7o
18.) 10
19.) 7
20.) 13°
21.) 11
22.) 25
23.) 0
24.) 2
25.) 1
26.) 19.1
27.) 196.9
28.) 13.1
29.) 2349.1
30.) resultant: 48.4; angle between larger force & resultant: 32o
31.) (a) imaginary
(b) imaginary (c) real, rational, and equal
33.) 1814400
34.) 76904685
35.) !"#
37.) 8x + 4
38.) 8b2 – 30b + 29
39.) ℎ!!  = ±  + 8
40.)  !!  =
!!!
!
41.) QIV
!"#
42.) 18.8 in
32.) 65780
36.) 55.9%
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