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  • Brainly User
2016-02-17T09:26:03+08:00
Given the measurement of three sides (SSS), use the Law of Cosines to find the angles.

Let x be the smallest angle in degrees.

Since 9 cm is the shortest side, the angle opposite it is the smallest.

                 (13)² + (17)² - (9)²
cos X =    -----------------------
                    2 (13) (17)
       
                 169 + 289 - 169
          =   -------------------------
                       442
 
                 377
          =    --------
                 442

          = 0.85294

cos ⁻¹ (0.85294) = 31.4671 or 31.5°

ANSWER:  The smallest angle is 31.5°.

Use the same formula to find the measurements of the other two angles.  The sum must be 180°. :-)

(Note:  I edited because at first I misread 9 cm as 19, it's blurred or shadowed. I found out it's only 9 when I checked again in enlarged photo.)
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