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The lengths of three sides of a triangle are 10 centimeters, 11 centimeters, and 13 centimeters. Find the measure of the smallest angle of the triangle.

Sagot :

mhanifa

Answer:

  • 48.4°

Step-by-step explanation:

The smallest angle is opposite to the smallest side.

Use the law of cosines to find the angle opposite to side with the length of 10 cm:

  • cos A = (b² + c² - a²)/(2bc)
  • cos x = (11² + 13² - 10²)/(2*11*13)
  • cos x = 190/286
  • cos x = 0.664 (rounded)
  • x = arccos (0.664)
  • x = 48.4° (rounded)

Use law of cosines

  • cosX=(b²+c²-a²)/2bc
  • cosX=(13²+11²-10²)/2(13)(11)
  • cosX=0.66
  • X=cos^{-1}(0.66)
  • X=48.4°
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