Math Doubts

Cosine value

Right angled triangle having 30 degrees angle

ΔGHI is a right angled triangle.

It is measured that

  • Length of the opposite side GI is GI  =  2.5 meters
  • Length of the adjacent side HI is HI  =  4.33 meters
  • Length of the hypotenuse is HG is HG  =  5 meters
  • The angle of the triangle is GHI  =  30°.

Now, calculate value of the cosine at angle 30° by considering the length of the adjacent side and length of the hypotenuse.

cos 30°  =  Length of the Adjacent sideLength of the Hypotenuse

⇒   cos 30°  =  HIHG

⇒   cos 30°  =  4.335

⇒   cos 30°  =  0.866

The value of cosine at the angle 30° is 0.866 for the triangle GHI.

Right angled triangle having 30 degrees angle

ΔFED is another right angled triangle and it is measured that,

  • The length of the opposite side DF is DF  =  3 meters
  • The length of the adjacent side EF is EF  =  5.196 meters
  • The length of the hypotenuse is ED is ED  =  6 meters
  • The angle of the triangle is FED  =  30°.

Repeat same procedure to calculate the value of cosine at an angle 30° for the right angled triangle FED.

cos 30°  =  Length of the Adjacent sideLength of the Hypotenuse

⇒   cos 30°  =  EFED

⇒   cos 30°  =  5.1966

⇒   cos 30°  =  0.866



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