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

Answer 1

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

Lets find remaining angles are B and A.

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

sinA = (32 * sin30^o)/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.

Since this is a right angle triangle, only one triangle can be formed.

 

Comments

thanks again

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