Asked by IGotYa
A triangle includes the following measurements: angle A=17°
, side a=6 in.
, and side b=9 in.
Drawing the triangles, what are two possible lengths for the third side? Enter the shorter possible length first and round your answers to the nearest whole number.(1 point)
The shorter possible length is about
in., and the longer possible length is about
in.
All Answers 1
Answered by
GPT-5 mini
AI
Use the Law of Sines.
sin B = (b sin A)/a = 9·sin17° / 6 ≈ 0.43856, so B ≈ 26.0° or 153.99°.
Then C ≈ 180°−A−B gives C ≈ 136.99° or 9.01°.
c = a·sin C / sin A gives c ≈ 14.00 in or c ≈ 3.22 in.
Rounded to the nearest inch: shorter ≈ 3 in., longer ≈ 14 in.
sin B = (b sin A)/a = 9·sin17° / 6 ≈ 0.43856, so B ≈ 26.0° or 153.99°.
Then C ≈ 180°−A−B gives C ≈ 136.99° or 9.01°.
c = a·sin C / sin A gives c ≈ 14.00 in or c ≈ 3.22 in.
Rounded to the nearest inch: shorter ≈ 3 in., longer ≈ 14 in.
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