Two sides of a triangle are 16.2 cm and 29.6 cm, with the included angle 106◦. What is angle opposite the side 16.2 cm?

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Answer 1 · 2016-12-02T17:37:01

The angle #A ~~ 24.6^@#

Let side #a = 16.2" cm"#
Let side #b = 29.6" cm"#
Let side #c = # the unknown side.

Let #angle A = # the unknown angle opposite side a.
Let #angle B = # the unknown angle opposite side b.
Let #angle C = 106^@#

Use the Law of Cosines to find the length of side c:

#c = sqrt(a^2 + b^2 - 2(a)(c)cos(C))#

#c = sqrt((16.2" cm")^2 + (29.6" cm")^2 - 2(16.2" cm")(29.6" cm")cos(106^@))#

#c ~~ 37.46" cm"#

Use the Law of Sines to find #angle A#

#sin(A)/a = sin(C)/c#

#sin(A) = sin(C)a/c#

#A = sin^-1(sin(C)a/c)#

#A = sin^-1(sin(106^@)(16.2" cm")/(37.46" cm"))#

#A ~~ 24.6^@#