Question

Having trouble solving this problem from my ACT prep bookIt is trigonometry

Answer 1

We need to convert 135.28º in degree, minute, and second measure.

In order to do so, notice that:

`135.28\degree=135\degree+0.28\degree`

Also,

`1\degree=60^(\prime)`

Thus, we have the proportion:

degrees minutes

1 60

0.28 x

Then:

`x=0.28\cdot60=16.8`

Thus:

`0.28\degree=16.8^(\prime)=16^(\prime)+0.8^(\prime)`

Now, notice that:

`1^(\prime)=60^(\doubleprime)`

Thus, we have the proportion:

minutes seconds

1 60

0.8 y

Then:

`y=0.8\cdot60=48`

Therefore:

`135.28\degree=135\degree16^(\prime)48^(\doubleprime)^{}`

And the first option is correct.