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.

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?

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.

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.

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?

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.

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