Mammoth Memory

Cosine examples

Example 1

If the hypotenuse is 1 metre long and `theta=35^@`, how long is the adjacent side?

How long is the opposite side if the angle is 45 degrees

Look up on the table/chart of cosine (angle) for `35^@` or look up cosine `35^@` on a calculator.

Angle

 

Adjacent distance (or cosine)

 

`35^@`

 

`0.8191 metres`

 

Answer:

Hypotenuse = 1 metre,

`theta=35^@`,

Therefore adjacent = 0.8191 metres

 

Example 2

If the hypotenuse is 1 metre long and `theta=45^@`, how long is the adjacent side?

How long is the adjacent side if the angle is 45 degrees

 

Look up on the table/chart of cosine (angle) for `45^@` or look up cosine `45^@` on a calculator.

Angle

 

Adjacent distance (or cosine)

 

`45^@`

 

`0.7071 metres`

 

Answer:

Hypotenuse = 1 metre,

`theta=45^@`,

Therefore adjacent = 0.7071 metres

  

Example 3

If the hypotenuse is 1 metre long, and the adjacent side is 0.8 metres long, what is the angle `theta`  ?

How long is the opposite side if the angle is 45 degrees

Look up on the table/chart of cosine (angle) for 0.8 metres and find the angle.

Angle

 

Adjacent distance (or cosine)

 

?

 

`0.8 metres`

The nearest = 36° = 0.809 metres  

But on a calculator if you put in 0.8 and press inverse cosin (cos-1), this gives you 36.86° (which is more accurate).

  

Example 4

If the hypotenuse is 2 metres long and `theta=45^@`, how long is the adjacent side?

How long is the adjacent side if the angle is 45 degrees and the hypotenuse is 2 meters

Look up on the table/chart of cosine (angle) for `45^@` or look up cosine `45^@` on a calculator.

Angle

 

Adjacent distance (or cosine)

 

`45^@`

 

`0.7071 metres`

But 0.7071 is for a 1m hypotenuse.

For a hypotenuse of 2m the adjacent would be twice as long.

Therefore `0.7071times2 = 1.4142`

 

Answer:

Hypotenuse = 2 metres,

`theta=45^@`,

Therefore adjacent = 1.4142 metres

 

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