Cosine examples
Example 1
If the hypotenuse is 1 metre long and `theta=35^@`, how long is the adjacent side?
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^@` 
`0.8192 metres` 
Answer:
Hypotenuse = 1 metre,
`theta=35^@`,
Therefore adjacent = 0.8192 metres
Example 2
If the hypotenuse is 1 metre long and `theta=45^@`, how long is the adjacent side?
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` ?
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 36.87° (which is more accurate).
Example 4
If the hypotenuse is 2 metres long and `theta=45^@`, how long is the adjacent side?
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
Cosine examples
Example 1
If the hypotenuse is 1 metre long and`theta=35^@`, how long is the adjacent side?
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?
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` ?
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?
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