Expert: Sherman D. - 3/12/2005

Question
solve each triangleABC. give angle measures to the nearest tenth of a degree and lengths in simplest radical form or to 2 significant digits.

1) Angle B=30 degrees, Angle C=45 degrees, b=9
2) Angle B=30 degrees, Angle A=135 degrees, b=4


Answer
1.)
Angle B = 30
Angle C = 45
b = 9

A + B + C = 180
A + 30 + 45 = 180
A + 75 = 180
A = 105

a/(sinA) = b/(sinB) = c/(sinC)

a/(sinA) = b/(sinB)
a/(sin(105)) = 9/(sin(30))
sin(30)a = 9sin(105)
a = (9sin(105))/(sin(30))
a = 9 * (sin(105)/sin(30))
a = 9 * 1.931851653
a = 17
or
a = 18sin(105)

b/(sinB) = c/(sinC)
9/(sin(30)) = c/(sin(45))
sin(30)c = 9sin(45)
c = (9sin(45))/(sin(30))
c = 9 * (sin(45)/sin(30))
c = 9 * 1.414213562
c = 13
or
c = 18sin(45)

ANS :
Angle A = 105°
Side a = 17
Side c = 13

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2.)
Angle B = 30
Angle A = 135
b = 4

A + B + C = 180
135 + 30 + C = 180
165 + C = 180
C = 15

a/(sinA) = b/(sinB) = c/(sinC)

a/(sinA) = b/(sinB)
a/(sin(135)) = 4/(sin(30))
sin(30)a = 4sin(135)
a = (4sin(135))/(sin(30))
a = 4 * (sin(135)/sin(30))
a = 4 * 1.414213562
a = 5.7
or
a = 8sin(135)

b/(sinB) = c/(sinC)
4/(sin(30)) = c/(sin(15))
sin(30)c = 4sin(15)
c = (4sin(15))/(sin(30))
c = 4 * (sin(15)/sin(30))
c = 4 * .51763809
c = 2.1
or
c = 8sin(15)

ANS :
Angle C = 15°
side a = 5.7
side c = 2.1

I got my info at http://mathworld.wolfram.com/LawofSines.html

as for the answers that i have in x * sin(y), that is just a simple way of putting it, but you are probably looking for the decimal form.