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State whether the offered measurements recognize zero, one, or two triangles. C = 30°, a = 32, c = 16 0 votestrigaskedJul 31, 2014in TRIGONOMETRYby Tdog79Pupil

angle C = 30o and sides a = 32, c = 16.

You are watching: State whether the given measurements determine zero, one, or two triangles. c = 30°, a = 32, c = 16

Lets uncover remaining angles room B and A.

Law the sines : c/sinC = a/sinA ⇒ sinA = (a * sinC) / c

sinA = (32 * sin30o)/16 = (32 * 1/2) / 16 = 16/16 = 1

A = sin^-1(1) = 90

Since sum of angles in a triangle = 180.

A+ B +C = 180.

Angle B = 180 - (A + B) = 180 - 30 - 90 = 60.

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Since this is a best angle triangle, only one triangle deserve to be formed.