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4.1 Find the function value using tables.
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(a) sin 56 34 (b) cos 19 45 (c) tan 77 12 (d) cot 40 36 (e) sec 23 47 0.8345; 8339 0.9412; 9417 4.4016; 43897 1.1667; 11708 1.0928; 10918 0.4(16) 0.5(10) 0.2(597) 0.6(68) 0.7(14) 8339 9417 11708 10918 6 5 119 41 10
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CHAPTER 4 Solution of Right Triangles
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(f) csc 60 4 (g) sin 46.35 (h) cos 18.29 (i) tan 82.19 (j) cot 13.84 (k) sec 29.71 (l) csc 11.08
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1.1539; 11547 0.7236; 7230 0.9495; 9500 7.2908; 72066 4.0591; 40713 1.1513; 11512 5.2035; 52408
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0.4(19) 0.5(12) 0.9(6) 0.9(936) 0.4(305) 0.1(12) 0.8(466)
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11547 7230 9500 6 5
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72066 40713 11512 52408
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4.2 In the manual solution, if the correction is 6.5, 13.5, 10.5, etc., we will round off so that the final result is an even number.
(a) sin 28 37 (b) cot 65 53 (c) cos 35 25 (d) sec 39 35 0.4790; 4772 0.4476; 4487 0.8150; 8158 1.2976; 12960 0.7(25) 0.3(35) 0.5(17) 0.5(31) 4772 4487 8158 12960 17.5 10.5 8.5 15.5 4789.5 4476.5 8149.5 12975.5
4.3 Find the function value using a calculator.
(a) sin 56 34 (b) cos 19 45 (c) tan 77 12 (d) cot 40 36 (e) sec 23 47 (f) csc 60 4 (g) sin 46.35 (h) cos 18.29 (i) tan 82.19 (j) cot 13.84 (k) sec 29.71 (l) csc 11.08 0.834527; sin (56 0.941176; cos (19 4.40152; tan (77 1.16672; 1/tan 40 36 1.09280; 1/cos 23 47 1.15393; 1/sin 60 4 0.723570 0.949480 7.29071 4.05904 1.15135 5.20347 34/60) 45/60) 12/60) 1/tan (40 1/cos (23 1/sin (60 36/60) 47/60) 4/60)
4.4 Find A to the nearest minute and to the nearest hundredth of a degree.
(a) sin A 43.00 (b) cos A 53.50 (c) tan A 43.40 (d) cot A 29.70 (e) sec A 64.40 (f) csc A 39.80 0.6826, A 6 (0.1 ) 13 0.5957, A 9 (0.1 ) 14 0.9470, A 13 (0.1 ) 33 1.7580, A 48 (0.1 ) 71 2.3198, A 54 (0.1 ) 84 1.5651, A 29 (0.1 ) 33 43 3 ; 43 0 43.00 0.05 9 (10 ) 24 35 (10 ) 55 24 (10 ) 119 110 (10 ) 140 40 (10 ) 55 53 30 4 :A 53.44 ; 6 (10 ) 21 43 0 3 :A 43.05 ;
53 26 ; 53 30 53.50 0.06
43 26 ; 43 20 43.40 0.04
43 20
6 :A
43.44 ;
29 38 ; 29 40 29.70 0.07
29 40
2 :A
29.63 ;
64 28 ; 64 20 64.40 0.06
64 20
8 :A
64.46 ;
39 43 ; 39 50 39.80 0.09
39 50
7: A
39.71 ;
CHAPTER 4 Solution of Right Triangles
35 10 and c 72.5.
4.5 Solve the right triangle in which A
B 90 35 10
54 50 . (See Fig. 4.1.) a/c b/c sin A cos A a b c sin A c cos A 72.5(0.5760) 72.5(0.8175) 41.8 59.3
Fig. 4.1
4.6 Solve the right triangle in which a
B 90 58 53
24.36 and A
58 53 .
31 7 . (See Fig. 4.2.) b/a cot A tan A csc A sin A b b c c a cot A a/tan A a csc A a/sin A 24.36(0.6036) 24.36/1.6567 24.36(1.1681) 24.36/0.8562 14.70 14.70 28.45 28.45
a/b c/a
Fig. 4.2
Solve the right triangle ABC in which a
tan A
43.9 24.3
43.9 and b
24.3. (See Fig. 4.3.)
61.0 and B 50.2 50.2 90 A 29.0 .
1.8066; A
61 0 and B c/a csc A sin A,
90 c c
29 0 , or A
a csc A a/sin A
43.9(1.1434) 43.9/0.8746
Fig. 4.3
CHAPTER 4 Solution of Right Triangles
4.8 Solve the right triangle ABC in which b
sin B
15.25 32.68
15.25 and c
90 B
32.68. (See Fig. 4.4.)
27.82 and A 28.90 28.90 90 B 62.18 .
0.4666; B
27 49 and A a/b cot B tan B a a
62 11 , or B 15.25(1.8953) 15.25/0.5276
b cot B b/tan B
Fig. 4.4
(NOTE: See App. 1, Geometry, for properties used in Probs. 4.9 to 4.11.)
4.9 The base of an isosceles triangle is 20.4 and the base angles are 48 40 . Find the equal sides and the altitude of the triangle.
In Fig. 4.5, BD is perpendicular to AC and bisects it. In the right triangle ABD, AB/AD or AD/AB DB/AD sec A cos A tan A AB AB DB 10.2(1.5141) 10.2/0.6604 10.2(1.1369) 15.4 15.4 11.6
Fig. 4.5
4.10 Considering the earth as a sphere of radius 3960 mi, find the radius r of the 40th parallel of latitude. Refer to Fig. 4.6.
In the right triangle OCB, / OBC Then Manual: r Calculator: r cos / OBC 3960 cos 40 3960 cos 40 40 and OB and 3033. 3033.53. 3960. r CB 3960 cos 40 CB/OB
3960(0.7660)
3960(0.766044)
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