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SUPPLEMENTARY PROBLEMS

1. (a) Solve the following oblique triangle ABC, given

a = 125, Ð A = 540 40' , Ð B = 650 10'

Answer :- b = 139, c = 133, Ð C = 600 10'

(b) a = 320, c = 475, A = 350 20'

Answer :- b = 552, Ð B = 850 30', Ð C = 590 10'

b' = 224, Ð B' = 230 50', Ð C' = 1200 50'

(c) Solve the triangle whose sides are respectively 52.8, 39.3 and 72.1

Answer :- Ð A = 450 44' , Ð B = 320 12', Ð C = 1020 4'

(d) In triangle ABC, a = 54 cms, b = 78 cms and c = 92 cm. Find the greatest angle.

(e) The sides of the triangle are 7 cms, 4 Ö 3 cms and Ö 13 cms. Find the smallest angles.

2. (a) A light house is 10 miles northwest of a dock. A ship leaves the dock at 9 A.M. and steams west at 12 miles / hour. At what time will it be 8 miles from the light house ?

(b) Two forces of 115 1b and 215 1b acting on an object have a resultant of magnitude 275 1b. Find the angle between the directions in which the given forces act .

Answer : - 700 50'

(c) In the regular hexagon shown. Find the length AC and AD if each side has length 6.23 units. Use the fact that in a regular hexagon, each angle is,

Answer : AC = 10.7907, AD = 12.4600



(d) Two planes take off from the same air port. The first one flies on a course of 220.10. The second one flies on a course of 154.40. After the first plane flies 362.4 kms, the course from the second plane is 83.50. How far is the second plane from the airport ?

Answer : 263.507 kms.


3. (a) Verify the identity (a - b) cos r /2 = c sin , which is known as Mollweide's formula.

(b) Prove that  

4. (a) Solve the triangle ABC if a = 12, b = 10 and a = 510

Answer :- b1 = 40.36 25 , b2 = 139.637 g1 = 88.6375, g2 =
-10.6370, c1 = 15.4367. Since negative angle g2 is impossible. There is only one solution. Check it by b < a.

(b) A small electronic component in the shape of a triangle with sides 6.23, 8.146 and 11.392 millimeters. Find the largest angle. Ans :- 104.031 0

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Index

3. 1 Solving Right Triangles
3. 2 Law of Cosines
3. 3 Law of Sines
3. 4 The Ambiguous Case of Law of Sines
3. 5 Areas of Triangles
Supplementary Problems

Chapter 4





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