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Answered

9. What is the measure
of the smallest angle in AABC with sides a = 7, b = 16 and c = 10 ?
A. 16.39°
B. 25.36°
C. 32.250
D. 57.75°

Sagot :

KANTOINEDOIXIN

LAW OF COSINES

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[tex] \large \bold{\blue{Question:}} [/tex] What is the measure of the smallest angle in ∆ABC with sides a = 7, b = 16 and c = 10 ?

  • A. 16.39°
  • B. 25.36°
  • C. 32.25°
  • D. 57.75°

[tex] \large \bold{\blue{Answer:}} \: \: \LARGE \tt \green{A. \ 16.39 \sf °} [/tex]

[tex] \large \bold{\blue{Reason:}} [/tex] Since the triangle gives three sides (SSS), we will be using the law of cosines.

» Remember that the opposite angle of the shortest side of a triangle was the smallest angle. In this case, since side (a) was the shortest side, we'll gonna find the measure of angle A.

  • [tex] \sf cos \: A = \frac{b² \ + \ c² \ - \ a²}{2bc} [/tex]

  • [tex] \sf cos \: A = \frac{16² \ + \ 10² \ - \ 7²}{2(16)(10)} [/tex]

  • [tex] \sf cos \: A = \frac{256 \ + \ 100 \ - \ 49}{2(16)(10)} [/tex]

  • [tex] \sf cos \: A = \frac{307}{320} [/tex]

  • [tex] \sf \angle A = cos^{-1}(\frac{307}{320}) [/tex]

  • [tex] \sf \angle A = 16.39° [/tex]

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