SUPPLEMENTARY PROBLEMS
1. (a) Solve the following oblique triangle ABC, given
a = 125, Ð A = 54^{0}
40' , Ð B = 65^{0} 10'
Answer : b = 139, c = 133, Ð
C = 60^{0} 10'
(b) a = 320, c = 475, A = 35^{0} 20'
Answer : b = 552, Ð B = 85^{0}
30', Ð C = 59^{0} 10'
b' = 224, Ð B' = 23^{0}
50', Ð C' = 120^{0} 50'
(c) Solve the triangle whose sides are respectively 52.8, 39.3
and 72.1
Answer : Ð A = 45^{0}
44' , Ð B = 32^{0} 12',
Ð C = 102^{0} 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 :  70^{0} 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 220.1^{0}. The second one flies on
a course of 154.4^{0}. After the first plane flies 362.4
kms, the course from the second plane is 83.5^{0}. 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
= 51^{0}
Answer : b_{1} = 40.36 25
, b_{2} = 139.637 g_{1}
= 88.6375, g_{2} =
10.6370, c_{1} = 15.4367. Since negative angle g_{2}
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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