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.