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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