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Determine if the given measurements determine 0,1, or 2 possible triangles.

Determine if the given measurements determine 0,1, or 2 possible triangles.-example-1
User Oxilumin
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1 Answer

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Answer: 1

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Step-by-step explanation

Let's use the law of sines to determine angle "A".

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

sin(A)/16.3 = sin(39.3)/24.1

sin(A) = 16.3*sin(39.3)/24.1

sin(A) = 0.428386 approximately

A = arcsin(0.428386) or A = 180-arcsin(0.428386)

A = 25.365175 or A = 154.634825

Both results are approximate.

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If A = 25.365175, then,

A+B+C = 180

B = 180-A-C

B = 180-25.365175-39.3

B = 115.334825

This result is in the interval 0 < B < 180, so we have a valid triangle here.

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If A = 154.634825, then,

A+B+C = 180

B = 180-A-C

B = 180-154.634825-39.3

B = -13.934825

This result is NOT in the interval 0 < B < 180, so a triangle cannot be formed when A = 154.634825 degrees.

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To summarize, a triangle is only possible when angle A = 25.365175 degrees approximately.

Therefore, only one triangle is possible.

A tool like GeoGebra can be used to confirm the answer.

User Qutax
by
8.1k points

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