Mammoth Memory

Sine examples

Example 1

How long is the opposite side if the angle is 35 degrees

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

 

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

Angle

 

Opposite distance (or sine)

 

`35^@`

 

`0.5735 metres`

Answer:

Hypotenuse = 1 metre,

`theta=35^@`,

Therefore, Opposite = 0.5735 metres.

 

Example 2

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

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

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

Angle

 

Opposite distance (or sine)

 

`45^@`

 

`0.7071 metres`

Answer:

Hypotenuse = 1 metre,

`theta=45^@`,

Therefore, Opposite = 0.7071 metres.

 

Example 3

If the hypotenuse is 1 metre long, and the opposite 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 sine (angle) for 0.8 metres and find the angle.

Angle

 

Opposite distance (or sine)

 

?

 

`0.8 metres`

The nearest = 54° = 0.809 metres. 

But on a calculator if you put in 0.8 and press inverse sin (sin-1), this gives you 53.13° (which is more accurate).

 

Example 4

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

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

 

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

Angle

 

Opposite distance (or sine)

 

`45^@`

 

`0.7071 metres`

 

But 0.7071 is for a 1m hypotenuse.

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

Therefore `0.7071times2=1.4142`

 

Answer:

Hypotenuse = 2 metres,

`theta=45^@`,

Therefore opposite = 1.4142 metres.

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